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Publisher: Springer-Verlag   (Total: 2335 journals)

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Showing 1 - 200 of 2335 Journals sorted alphabetically
3D Research     Hybrid Journal   (Followers: 19, SJR: 0.214, h-index: 10)
4OR: A Quarterly J. of Operations Research     Hybrid Journal   (Followers: 9, SJR: 1.073, h-index: 25)
AAPS J.     Hybrid Journal   (Followers: 16, SJR: 1.192, h-index: 74)
AAPS PharmSciTech     Hybrid Journal   (Followers: 6, SJR: 0.718, h-index: 54)
Abdominal Imaging     Hybrid Journal   (Followers: 16, SJR: 0.723, h-index: 60)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2, SJR: 0.447, h-index: 12)
Academic Psychiatry     Full-text available via subscription   (Followers: 22, SJR: 0.492, h-index: 32)
Academic Questions     Hybrid Journal   (Followers: 7, SJR: 0.135, h-index: 6)
Accreditation and Quality Assurance: J. for Quality, Comparability and Reliability in Chemical Measurement     Hybrid Journal   (Followers: 26, SJR: 0.378, h-index: 30)
Acoustical Physics     Hybrid Journal   (Followers: 10, SJR: 0.355, h-index: 20)
Acta Analytica     Hybrid Journal   (Followers: 7, SJR: 0.387, h-index: 6)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1, SJR: 0.624, h-index: 34)
Acta Biotheoretica     Hybrid Journal   (Followers: 5, SJR: 0.419, h-index: 25)
Acta Diabetologica     Hybrid Journal   (Followers: 14, SJR: 1.318, h-index: 46)
Acta Endoscopica     Hybrid Journal   (Followers: 1, SJR: 0.113, h-index: 8)
acta ethologica     Hybrid Journal   (Followers: 4, SJR: 0.465, h-index: 23)
Acta Geochimica     Hybrid Journal   (Followers: 3)
Acta Geodaetica et Geophysica     Hybrid Journal   (Followers: 1, SJR: 0.294, h-index: 13)
Acta Geotechnica     Hybrid Journal   (Followers: 6, SJR: 1.818, h-index: 22)
Acta Informatica     Hybrid Journal   (Followers: 5, SJR: 0.524, h-index: 32)
Acta Mathematica     Hybrid Journal   (Followers: 10, SJR: 8.021, h-index: 47)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2, SJR: 0.53, h-index: 29)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5, SJR: 0.406, h-index: 30)
Acta Mathematica Vietnamica     Hybrid Journal   (SJR: 0.451, h-index: 5)
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal   (SJR: 0.22, h-index: 20)
Acta Mechanica     Hybrid Journal   (Followers: 18, SJR: 0.898, h-index: 52)
Acta Mechanica Sinica     Hybrid Journal   (Followers: 4, SJR: 0.426, h-index: 29)
Acta Metallurgica Sinica (English Letters)     Hybrid Journal   (Followers: 5, SJR: 0.525, h-index: 18)
Acta Meteorologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.524, h-index: 14)
Acta Neurochirurgica     Hybrid Journal   (Followers: 7, SJR: 0.833, h-index: 73)
Acta Neurologica Belgica     Hybrid Journal   (SJR: 0.348, h-index: 27)
Acta Neuropathologica     Hybrid Journal   (Followers: 3, SJR: 6.61, h-index: 117)
Acta Oceanologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.295, h-index: 17)
Acta Parasitologica     Hybrid Journal   (Followers: 9, SJR: 0.581, h-index: 28)
Acta Physiologiae Plantarum     Hybrid Journal   (Followers: 2, SJR: 0.551, h-index: 39)
Acta Politica     Hybrid Journal   (Followers: 13, SJR: 0.658, h-index: 20)
adhäsion KLEBEN & DICHTEN     Hybrid Journal   (Followers: 5, SJR: 0.103, h-index: 4)
ADHD Attention Deficit and Hyperactivity Disorders     Hybrid Journal   (Followers: 20, SJR: 0.871, h-index: 15)
Adhesion Adhesives & Sealants     Hybrid Journal   (Followers: 7)
Administration and Policy in Mental Health and Mental Health Services Research     Partially Free   (Followers: 15, SJR: 0.795, h-index: 40)
Adsorption     Hybrid Journal   (Followers: 4, SJR: 0.774, h-index: 52)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3, SJR: 0.319, h-index: 15)
Advances in Atmospheric Sciences     Hybrid Journal   (Followers: 34, SJR: 0.959, h-index: 44)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15, SJR: 1.255, h-index: 44)
Advances in Contraception     Hybrid Journal   (Followers: 2)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 48, SJR: 1.113, h-index: 14)
Advances in Gerontology     Partially Free   (Followers: 7, SJR: 0.141, h-index: 3)
Advances in Health Sciences Education     Hybrid Journal   (Followers: 23, SJR: 1.397, h-index: 42)
Advances in Manufacturing     Hybrid Journal   (Followers: 3, SJR: 0.2, h-index: 4)
Advances in Polymer Science     Hybrid Journal   (Followers: 40, SJR: 0.637, h-index: 89)
Advances in Therapy     Hybrid Journal   (Followers: 6, SJR: 0.79, h-index: 44)
Aegean Review of the Law of the Sea and Maritime Law     Hybrid Journal   (Followers: 7)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2, SJR: 0.882, h-index: 23)
Aerobiologia     Hybrid Journal   (Followers: 1, SJR: 0.511, h-index: 36)
Aesthetic Plastic Surgery     Hybrid Journal   (Followers: 8, SJR: 0.821, h-index: 49)
African Archaeological Review     Hybrid Journal   (Followers: 14, SJR: 0.612, h-index: 24)
Afrika Matematika     Hybrid Journal   (Followers: 1, SJR: 0.248, h-index: 6)
AGE     Hybrid Journal   (Followers: 7, SJR: 1.358, h-index: 33)
Ageing Intl.     Hybrid Journal   (Followers: 6, SJR: 0.337, h-index: 10)
Aggiornamenti CIO     Hybrid Journal   (Followers: 1)
Aging Clinical and Experimental Research     Hybrid Journal   (Followers: 3, SJR: 0.529, h-index: 55)
Agricultural Research     Hybrid Journal   (Followers: 3)
Agriculture and Human Values     Hybrid Journal   (Followers: 12, SJR: 1.197, h-index: 49)
Agroforestry Systems     Hybrid Journal   (Followers: 20, SJR: 0.64, h-index: 56)
Agronomy for Sustainable Development     Hybrid Journal   (Followers: 10, SJR: 1.732, h-index: 59)
AI & Society     Hybrid Journal   (Followers: 7, SJR: 0.171, h-index: 19)
AIDS and Behavior     Hybrid Journal   (Followers: 13, SJR: 2.006, h-index: 71)
Air Quality, Atmosphere & Health     Hybrid Journal   (Followers: 2, SJR: 0.706, h-index: 19)
Akupunktur & Aurikulomedizin     Full-text available via subscription   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2, SJR: 0.566, h-index: 18)
Algebra Universalis     Hybrid Journal   (Followers: 2, SJR: 0.388, h-index: 22)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1, SJR: 0.868, h-index: 20)
Algorithmica     Hybrid Journal   (Followers: 7, SJR: 0.898, h-index: 56)
Allergo J.     Full-text available via subscription   (Followers: 1, SJR: 0.183, h-index: 20)
Allergo J. Intl.     Hybrid Journal   (Followers: 2)
Alpine Botany     Hybrid Journal   (Followers: 3, SJR: 0.729, h-index: 20)
ALTEX : Alternatives to Animal Experimentation     Open Access   (Followers: 3, SJR: 1.392, h-index: 32)
AMBIO     Hybrid Journal   (Followers: 14, SJR: 1.094, h-index: 87)
American J. of Cardiovascular Drugs     Hybrid Journal   (Followers: 10, SJR: 0.864, h-index: 39)
American J. of Community Psychology     Hybrid Journal   (Followers: 24, SJR: 1.237, h-index: 83)
American J. of Criminal Justice     Hybrid Journal   (Followers: 5, SJR: 0.634, h-index: 13)
American J. of Cultural Sociology     Hybrid Journal   (Followers: 11, SJR: 0.283, h-index: 3)
American J. of Dance Therapy     Hybrid Journal   (Followers: 4, SJR: 0.175, h-index: 13)
American J. of Potato Research     Hybrid Journal   (Followers: 2, SJR: 0.558, h-index: 35)
American J. of Psychoanalysis     Hybrid Journal   (Followers: 20, SJR: 0.293, h-index: 13)
American Sociologist     Hybrid Journal   (Followers: 10, SJR: 0.18, h-index: 13)
Amino Acids     Hybrid Journal   (Followers: 8, SJR: 1.362, h-index: 83)
AMS Review     Partially Free   (Followers: 4)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 5, SJR: 0.21, h-index: 37)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4, SJR: 0.665, h-index: 7)
Analysis in Theory and Applications     Hybrid Journal  
Analysis of Verbal Behavior     Hybrid Journal   (Followers: 4)
Analytical and Bioanalytical Chemistry     Hybrid Journal   (Followers: 32, SJR: 1.096, h-index: 123)
Anatomical Science Intl.     Hybrid Journal   (Followers: 2, SJR: 0.301, h-index: 26)
Angewandte Schmerztherapie und Palliativmedizin     Hybrid Journal  
Angiogenesis     Hybrid Journal   (Followers: 3, SJR: 2.212, h-index: 69)
Animal Cognition     Hybrid Journal   (Followers: 13, SJR: 1.122, h-index: 55)
Annales françaises de médecine d'urgence     Hybrid Journal   (Followers: 1, SJR: 0.156, h-index: 4)
Annales Henri Poincaré     Hybrid Journal   (Followers: 3, SJR: 1.377, h-index: 32)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annali dell'Universita di Ferrara     Hybrid Journal   (SJR: 0.504, h-index: 14)
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1, SJR: 1.167, h-index: 26)
Annals of Behavioral Medicine     Hybrid Journal   (Followers: 10, SJR: 2.112, h-index: 98)
Annals of Biomedical Engineering     Hybrid Journal   (Followers: 18, SJR: 1.182, h-index: 94)
Annals of Combinatorics     Hybrid Journal   (Followers: 3, SJR: 0.849, h-index: 15)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Dyslexia     Hybrid Journal   (Followers: 9, SJR: 0.857, h-index: 40)
Annals of Finance     Hybrid Journal   (Followers: 27, SJR: 0.686, h-index: 14)
Annals of Forest Science     Hybrid Journal   (Followers: 4, SJR: 0.929, h-index: 57)
Annals of Global Analysis and Geometry     Hybrid Journal   (Followers: 1, SJR: 1.136, h-index: 23)
Annals of Hematology     Hybrid Journal   (Followers: 13, SJR: 1.117, h-index: 62)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6, SJR: 0.593, h-index: 42)
Annals of Microbiology     Hybrid Journal   (Followers: 9, SJR: 0.402, h-index: 26)
Annals of Nuclear Medicine     Hybrid Journal   (Followers: 5, SJR: 0.68, h-index: 45)
Annals of Operations Research     Hybrid Journal   (Followers: 8, SJR: 1.186, h-index: 78)
Annals of Regional Science     Hybrid Journal   (Followers: 7, SJR: 0.405, h-index: 42)
Annals of Software Engineering     Hybrid Journal   (Followers: 12)
Annals of Solid and Structural Mechanics     Hybrid Journal   (Followers: 9, SJR: 0.553, h-index: 8)
Annals of Surgical Oncology     Hybrid Journal   (Followers: 11, SJR: 1.902, h-index: 127)
Annals of Telecommunications     Hybrid Journal   (Followers: 7, SJR: 0.315, h-index: 25)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1, SJR: 0.931, h-index: 31)
Antonie van Leeuwenhoek     Hybrid Journal   (Followers: 5, SJR: 0.992, h-index: 87)
Apidologie     Hybrid Journal   (Followers: 4, SJR: 1.14, h-index: 57)
APOPTOSIS     Hybrid Journal   (Followers: 7, SJR: 1.554, h-index: 87)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2, SJR: 0.354, h-index: 27)
Applications of Mathematics     Hybrid Journal   (Followers: 1, SJR: 0.274, h-index: 20)
Applied Biochemistry and Biotechnology     Hybrid Journal   (Followers: 44, SJR: 0.575, h-index: 80)
Applied Biochemistry and Microbiology     Hybrid Journal   (Followers: 17, SJR: 0.267, h-index: 26)
Applied Categorical Structures     Hybrid Journal   (Followers: 2, SJR: 0.361, h-index: 21)
Applied Composite Materials     Hybrid Journal   (Followers: 45, SJR: 0.705, h-index: 35)
Applied Entomology and Zoology     Partially Free   (Followers: 2, SJR: 0.554, h-index: 34)
Applied Geomatics     Hybrid Journal   (Followers: 3, SJR: 0.323, h-index: 9)
Applied Geophysics     Hybrid Journal   (Followers: 7, SJR: 0.541, h-index: 13)
Applied Intelligence     Hybrid Journal   (Followers: 13, SJR: 0.777, h-index: 43)
Applied Magnetic Resonance     Hybrid Journal   (Followers: 3, SJR: 0.358, h-index: 34)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4, SJR: 0.955, h-index: 33)
Applied Mathematics - A J. of Chinese Universities     Hybrid Journal   (SJR: 0.275, h-index: 8)
Applied Mathematics and Mechanics     Hybrid Journal   (Followers: 4, SJR: 0.37, h-index: 26)
Applied Microbiology and Biotechnology     Hybrid Journal   (Followers: 61, SJR: 1.262, h-index: 161)
Applied Physics A     Hybrid Journal   (Followers: 8, SJR: 0.535, h-index: 121)
Applied Physics B: Lasers and Optics     Hybrid Journal   (Followers: 22, SJR: 0.983, h-index: 104)
Applied Psychophysiology and Biofeedback     Hybrid Journal   (Followers: 6, SJR: 0.677, h-index: 47)
Applied Research in Quality of Life     Hybrid Journal   (Followers: 10, SJR: 0.288, h-index: 15)
Applied Solar Energy     Hybrid Journal   (Followers: 16, SJR: 0.251, h-index: 6)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4, SJR: 0.351, h-index: 9)
Aquaculture Intl.     Hybrid Journal   (Followers: 21, SJR: 0.613, h-index: 40)
Aquarium Sciences and Conservation     Hybrid Journal   (Followers: 1)
Aquatic Ecology     Hybrid Journal   (Followers: 31, SJR: 0.646, h-index: 44)
Aquatic Geochemistry     Hybrid Journal   (Followers: 3, SJR: 0.764, h-index: 39)
Aquatic Sciences     Hybrid Journal   (Followers: 12, SJR: 1.172, h-index: 53)
Arabian J. for Science and Engineering     Hybrid Journal   (Followers: 5, SJR: 0.345, h-index: 20)
Arabian J. of Geosciences     Hybrid Journal   (Followers: 1, SJR: 0.417, h-index: 16)
Archaeological and Anthropological Sciences     Hybrid Journal   (Followers: 21, SJR: 1.056, h-index: 15)
Archaeologies     Hybrid Journal   (Followers: 12, SJR: 0.397, h-index: 13)
Archiv der Mathematik     Hybrid Journal   (Followers: 1, SJR: 0.597, h-index: 29)
Archival Science     Hybrid Journal   (Followers: 51, SJR: 0.804, h-index: 22)
Archive for History of Exact Sciences     Hybrid Journal   (Followers: 7, SJR: 0.28, h-index: 15)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1, SJR: 0.946, h-index: 23)
Archive for Rational Mechanics and Analysis     Hybrid Journal   (SJR: 4.091, h-index: 66)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4, SJR: 0.865, h-index: 40)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4, SJR: 2.841, h-index: 40)
Archives of Dermatological Research     Hybrid Journal   (Followers: 6, SJR: 0.9, h-index: 65)
Archives of Environmental Contamination and Toxicology     Hybrid Journal   (Followers: 10, SJR: 0.846, h-index: 84)
Archives of Gynecology and Obstetrics     Hybrid Journal   (Followers: 16, SJR: 0.695, h-index: 47)
Archives of Microbiology     Hybrid Journal   (Followers: 8, SJR: 0.702, h-index: 85)
Archives of Orthopaedic and Trauma Surgery     Hybrid Journal   (Followers: 8, SJR: 1.039, h-index: 56)
Archives of Osteoporosis     Hybrid Journal   (Followers: 2, SJR: 1.092, h-index: 13)
Archives of Sexual Behavior     Hybrid Journal   (Followers: 9, SJR: 1.198, h-index: 74)
Archives of Toxicology     Hybrid Journal   (Followers: 16, SJR: 1.595, h-index: 76)
Archives of Virology     Hybrid Journal   (Followers: 4, SJR: 1.086, h-index: 90)
Archives of Women's Mental Health     Hybrid Journal   (Followers: 13, SJR: 1.264, h-index: 50)
Archivio di Ortopedia e Reumatologia     Hybrid Journal  
Archivum Immunologiae et Therapiae Experimentalis     Hybrid Journal   (Followers: 2, SJR: 1.2, h-index: 42)
ArgoSpine News & J.     Hybrid Journal   (SJR: 0.102, h-index: 3)
Argumentation     Hybrid Journal   (Followers: 4, SJR: 0.295, h-index: 18)
Arid Ecosystems     Hybrid Journal   (Followers: 3)
Arkiv för Matematik     Hybrid Journal   (Followers: 1, SJR: 0.948, h-index: 22)
Arnold Mathematical J.     Hybrid Journal   (Followers: 1)
Arthropod-Plant Interactions     Hybrid Journal   (Followers: 2, SJR: 0.797, h-index: 17)
Arthroskopie     Hybrid Journal   (Followers: 1, SJR: 0.145, h-index: 8)
Artificial Intelligence and Law     Hybrid Journal   (Followers: 8, SJR: 0.288, h-index: 25)
Artificial Intelligence Review     Hybrid Journal   (Followers: 15, SJR: 0.948, h-index: 48)
Artificial Life and Robotics     Hybrid Journal   (Followers: 8, SJR: 0.231, h-index: 14)
Asia Europe J.     Hybrid Journal   (Followers: 4, SJR: 0.247, h-index: 9)
Asia Pacific Education Review     Hybrid Journal   (Followers: 9, SJR: 0.371, h-index: 17)
Asia Pacific J. of Management     Hybrid Journal   (Followers: 11, SJR: 1.676, h-index: 50)
Asia-Pacific Education Researcher     Hybrid Journal   (Followers: 11, SJR: 0.353, h-index: 13)
Asia-Pacific Financial Markets     Hybrid Journal   (Followers: 2, SJR: 0.19, h-index: 15)
Asia-Pacific J. of Atmospheric Sciences     Hybrid Journal   (Followers: 20, SJR: 1.006, h-index: 14)
Asian Business & Management     Hybrid Journal   (Followers: 7, SJR: 0.41, h-index: 10)
Asian J. of Business Ethics     Hybrid Journal   (Followers: 7)
Asian J. of Criminology     Hybrid Journal   (Followers: 5, SJR: 0.263, h-index: 8)
AStA Advances in Statistical Analysis     Hybrid Journal   (Followers: 2, SJR: 0.681, h-index: 15)
AStA Wirtschafts- und Sozialstatistisches Archiv     Hybrid Journal   (Followers: 5, SJR: 0.195, h-index: 5)
ästhetische dermatologie & kosmetologie     Full-text available via subscription  
Astronomy and Astrophysics Review     Hybrid Journal   (Followers: 21, SJR: 4.511, h-index: 44)
Astronomy Letters     Hybrid Journal   (Followers: 19, SJR: 0.58, h-index: 30)
Astronomy Reports     Hybrid Journal   (Followers: 12, SJR: 0.473, h-index: 23)
Astrophysical Bulletin     Hybrid Journal   (Followers: 2, SJR: 0.469, h-index: 11)
Astrophysics     Hybrid Journal   (Followers: 22, SJR: 0.243, h-index: 11)

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Journal Cover Advances in Computational Mathematics
  [SJR: 1.255]   [H-I: 44]   [15 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1572-9044 - ISSN (Online) 1019-7168
   Published by Springer-Verlag Homepage  [2335 journals]
  • Hierarchical spline spaces: quasi-interpolants and local approximation
    • Authors: Hendrik Speleers
      Pages: 235 - 255
      Abstract: Abstract A local approximation study is presented for hierarchical spline spaces. Such spaces are composed of a hierarchy of nested spaces and provide a flexible framework for local refinement in any dimensionality. We provide approximation estimates for general hierarchical quasi-interpolants expressed in terms of the truncated hierarchical basis. Under some mild assumptions, we prove that such hierarchical quasi-interpolants and their derivatives possess optimal local approximation power in the general q-norm with \(1\leq q\leq \infty \) . In addition, we detail a specific family of hierarchical quasi-interpolants defined on uniform hierarchical meshes in any dimensionality. The construction is based on cardinal B-splines of degree p and central factorial numbers of the first kind. It guarantees polynomial reproduction of degree p and it requires only function evaluations at grid points (odd p) or half-grid points (even p). This results in good approximation properties at a very low cost, and is illustrated with some numerical experiments.
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-016-9483-y
      Issue No: Vol. 43, No. 2 (2017)
  • Reduced basis methods with adaptive snapshot computations
    • Authors: Mazen Ali; Kristina Steih; Karsten Urban
      Pages: 257 - 294
      Abstract: Abstract We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot (i.e., parameter-dependent) do not permit the standard RB ‘truth space’, but allow for error estimation of the RB approximation with respect to the exact solution of the considered parameterized partial differential equation. The residual-based a posteriori error estimators are computed by an adaptive dual wavelet expansion, which allows us to compute a surrogate of the dual norm of the residual. The resulting adaptive RBM is analyzed. We show the convergence of the resulting adaptive greedy method. Numerical experiments for stationary and instationary problems underline the potential of this approach.
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-016-9485-9
      Issue No: Vol. 43, No. 2 (2017)
  • Microlocal analysis of edge flatness through directional multiscale
    • Authors: Kanghui Guo; Demetrio Labate
      Pages: 295 - 318
      Abstract: Abstract Edges and surface boundaries are often the most relevant features in images and multidimensional data. It is well known that multiscale methods including wavelets and their more sophisticated multidimensional siblings offer a powerful tool for the analysis and detection of such sets. Among such methods, the continuous shearlet transform has been especially successful. This method combines anisotropic scaling and directional sensitivity controlled by shear transformations in order to precisely identify not only the location of edges and boundary points but also edge orientation and corner points. In this paper, we show that this framework can be made even more flexible by controlling the scaling parameter of the anisotropic dilation matrix and considering non-parabolic scaling. We prove that, using ‘higher-than-parabolic’ scaling, the modified shearlet transform is also able to estimate the degree of local flatness of an edge or surface boundary, providing more detailed information about the geometry of edge and boundary points.
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-016-9486-8
      Issue No: Vol. 43, No. 2 (2017)
  • The practical Gauss type rules for Hadamard finite-part integrals using
           Puiseux expansions
    • Authors: Tongke Wang; Zhiyue Zhang; Zhifang Liu
      Pages: 319 - 350
      Abstract: Abstract A general framework is constructed for efficiently and stably evaluating the Hadamard finite-part integrals by composite quadrature rules. Firstly, the integrands are assumed to have the Puiseux expansions at the endpoints with arbitrary algebraic and logarithmic singularities. Secondly, the Euler-Maclaurin expansion of a general composite quadrature rule is obtained directly by using the asymptotic expansions of the partial sums of the Hurwitz zeta function and the generalized Stieltjes constant, which shows that the standard numerical integration formula is not convergent for computing the Hadamard finite-part integrals. Thirdly, the standard quadrature formula is recast in two steps. In step one, the singular part of the integrand is integrated analytically and in step two, the regular integral of the remaining part is evaluated using the standard composite quadrature rule. In this stage, a threshold is introduced such that the function evaluations in the vicinity of the singularity are intentionally excluded, where the threshold is determined by analyzing the roundoff errors caused by the singular nature of the integrand. Fourthly, two practical algorithms are designed for evaluating the Hadamard finite-part integrals by applying the Gauss-Legendre and Gauss-Kronrod rules to the proposed framework. Practical error indicator and implementation involved in the Gauss-Legendre rule are addressed. Finally, some typical examples are provided to show that the algorithms can be used to effectively evaluate the Hadamard finite-part integrals over finite or infinite intervals.
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-016-9487-7
      Issue No: Vol. 43, No. 2 (2017)
  • An integral equation technique for scattering problems with mixed boundary
    • Authors: Adrianna Gillman
      Pages: 351 - 364
      Abstract: Abstract This paper presents an integral formulation for Helmholtz problems with mixed boundary conditions. Unlike most integral equation techniques for mixed boundary value problems, the proposed method uses a global boundary charge density. As a result, Calderón identities can be utilized to avoid the use of hypersingular integral operators. Numerical results illustrate the performance of the proposed solution technique.
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-016-9488-6
      Issue No: Vol. 43, No. 2 (2017)
  • Homotopy analysis Sumudu transform method for time—fractional third
           order dispersive partial differential equation
    • Authors: Rishi Kumar Pandey; Hradyesh Kumar Mishra
      Pages: 365 - 383
      Abstract: Abstract In this article, we apply the newly introduced numerical method which is a combination of Sumudu transforms and Homotopy analysis method for the solution of time fractional third order dispersive type PDE equations. It is also discussed generalized algorithm, absolute convergence and analytic result of the finite number of independent variables including time variable.
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-016-9489-5
      Issue No: Vol. 43, No. 2 (2017)
  • Piecewise spectral collocation method for system of Volterra integral
    • Authors: Zhendong Gu
      Pages: 385 - 409
      Abstract: Abstract The main purpose of this paper is to investigate the piecewise spectral collocation method for system of Volterra integral equations. The provided convergence analysis shows that the presented method performs better than global spectral collocation method and piecewise polynomial collocation method. Numerical experiments are carried out to confirm these theoretical results.
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-016-9490-z
      Issue No: Vol. 43, No. 2 (2017)
  • QTT-finite-element approximation for multiscale problems I: model problems
           in one dimension
    • Authors: Vladimir Kazeev; Ivan Oseledets; Maxim Rakhuba; Christoph Schwab
      Pages: 411 - 442
      Abstract: Abstract Tensor-compressed numerical solution of elliptic multiscale-diffusion and high frequency scattering problems is considered. For either problem class, solutions exhibit multiple length scales governed by the corresponding scale parameter: the scale of oscillations of the diffusion coefficient or smallest wavelength, respectively. As is well-known, this imposes a scale-resolution requirement on the number of degrees of freedom required to accurately represent the solutions in standard finite-element (FE) discretizations. Low-order FE methods are by now generally perceived unsuitable for high-frequency coefficients in diffusion problems and high wavenumbers in scattering problems. Accordingly, special techniques have been proposed instead (such as numerical homogenization, heterogeneous multiscale method, oversampling, etc.) which require, in some form, a-priori information on the microstructure of the solution. We analyze the approximation properties of tensor-formatted, conforming first-order FE methods for scale resolution in multiscale problems without a-priori information. The FE methods are based on the dynamic extraction of principal components from stiffness matrices, load and solution vectors by the quantized tensor train (QTT) decomposition. For prototypical model problems, we prove that this approach, by means of the QTT reparametrization of the FE space, allows to identify effective degrees of freedom to replace the degrees of freedom of a uniform “virtual” (i.e. never directly accessed) mesh, whose number may be prohibitively large to realize computationally. Precisely, solutions of model elliptic homogenization and high-frequency acoustic scattering problems are proved to admit QTT-structured approximations whose number of effective degrees of freedom required to reach a prescribed approximation error scales polylogarithmically with respect to the reciprocal of the target Sobolev-norm accuracy ε with only a mild dependence on the scale parameter. No a-priori information on the nature of the problems and intrinsic length scales of the solution is required in the numerical realization of the presently proposed QTT-structured approach. Although only univariate model multiscale problems are analyzed in the present paper, QTT structured algorithms are applicable also in several variables. Detailed numerical experiments confirm the theoretical bounds. As a corollary of our analysis, we prove that for the mentioned model problems, the Kolmogorov n-widths of solution sets are exponentially small for analytic data, independently of the problems’ scale parameters. That implies, in particular, the exponential convergence of reduced basis techniques which is scale-robust, i.e., independent of the scale parameter in the problem.
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-016-9491-y
      Issue No: Vol. 43, No. 2 (2017)
  • Explicit constructions and properties of generalized shift-invariant
           systems in L 2 ( ℝ ) $L^{2}(\mathbb {R})$
    • Authors: Ole Christensen; Marzieh Hasannasab; Jakob Lemvig
      Pages: 443 - 472
      Abstract: Abstract Generalized shift-invariant (GSI) systems, originally introduced by Hernández et al. and Ron and Shen, provide a common frame work for analysis of Gabor systems, wavelet systems, wave packet systems, and other types of structured function systems. In this paper we analyze three important aspects of such systems. First, in contrast to the known cases of Gabor frames and wavelet frames, we show that for a GSI system forming a frame, the Calderón sum is not necessarily bounded by the lower frame bound. We identify a technical condition implying that the Calderón sum is bounded by the lower frame bound and show that under a weak assumption the condition is equivalent with the local integrability condition introduced by Hernández et al. Second, we provide explicit and general constructions of frames and dual pairs of frames having the GSI-structure. In particular, the setup applies to wave packet systems and in contrast to the constructions in the literature, these constructions are not based on characteristic functions in the Fourier domain. Third, our results provide insight into the local integrability condition (LIC).
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-016-9492-x
      Issue No: Vol. 43, No. 2 (2017)
  • A matrix method for fractional Sturm-Liouville problems on bounded domain
    • Authors: Paolo Ghelardoni; Cecilia Magherini
      Abstract: Abstract A matrix method for the solution of direct fractional Sturm-Liouville problems (SLPs) on bounded domains is proposed where the fractional derivative is defined in the Riesz sense. The scheme is based on the application of the Galerkin spectral method of orthogonal polynomials. The order of convergence of the eigenvalue approximations with respect to the matrix size is studied. Some numerical examples that confirm the theory and prove the competitiveness of the approach are finally presented.
      PubDate: 2017-03-24
      DOI: 10.1007/s10444-017-9529-9
  • Constructing radial kernels with higher-order generalized Strang-Fix
    • Authors: Wenwu Gao; Zongmin Wu
      Abstract: Abstract The paper provides an approach for constructing multivariate radial kernels satisfying higher-order generalized Strang-Fix conditions from a given univariate generator. There are three key features of the approach. First, the kernels are explicitly expressed only by the derivatives of the f-form of the generator without computing any Fourier transforms. Second, it includes the radial kernels with the highest-order generalized Strang-Fix conditions. Finally, it requires only computing univariate derivatives of the f-form. Therefore, the approach is simple, efficient and easy to implement. As examples, the paper constructs radial kernels from some commonly used generators, including the Gaussian functions, the inverse multiquadric functions and compactly supported positive definite functions.
      PubDate: 2017-03-24
      DOI: 10.1007/s10444-017-9528-x
  • A simple finite element method for the Stokes equations
    • Authors: Lin Mu; Xiu Ye
      Abstract: Abstract The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.
      PubDate: 2017-03-21
      DOI: 10.1007/s10444-017-9526-z
  • Families of univariate and bivariate subdivision schemes originated from
           quartic B-spline
    • Authors: Ghulam Mustafa; Rabia Hameed
      Abstract: Abstract Families of parameter dependent univariate and bivariate subdivision schemes are presented in this paper. These families are new variants of the Lane-Riesenfeld algorithm. So the subdivision algorithms consist of both refining and smoothing steps. In refining step, we use the quartic B-spline based subdivision schemes. In smoothing step, we average the adjacent points. The bivariate schemes are the non-tensor product version of our univariate schemes. Moreover, for odd and even number of smoothing steps, we get the primal and dual schemes respectively. Higher regularity of the schemes can be achieved by increasing the number of smoothing steps. These schemes can be nicely generalized to contain local shape parameters that allow the user to adjust locally the shape of the limit curve/surface.
      PubDate: 2017-03-13
      DOI: 10.1007/s10444-017-9519-y
  • A note on Taylor boundary conditions for accurate image restoration
    • Authors: Pietro Dell’Acqua
      Abstract: Abstract In recent years, several efforts were made in order to introduce boundary conditions for deblurring problems that allow to get accurate reconstructions. This resulted in the birth of Reflective, Anti-Reflective and Mean boundary conditions, which are all based on the idea of guaranteeing the continuity of the signal/image outside the boundary. Here we propose new boundary conditions that are obtained by suitably combining Taylor series and finite difference approximations. Moreover, we show that also Anti-Reflective and Mean boundary conditions can be attributed to the same framework. Numerical results show that, in case of low levels of noise and blurs able to perform a suitable smoothing effect on the original image (e.g. Gaussian blur), the proposed boundary conditions lead to a significant improvement of the restoration accuracy with respect to those available in the literature.
      PubDate: 2017-03-10
      DOI: 10.1007/s10444-017-9525-0
  • A fully diagonalized spectral method using generalized Laguerre functions
           on the half line
    • Authors: Fu-Jun Liu; Zhong-Qing Wang; Hui-Yuan Li
      Abstract: Abstract A fully diagonalized spectral method using generalized Laguerre functions is proposed and analyzed for solving elliptic equations on the half line. We first define the generalized Laguerre functions which are complete and mutually orthogonal with respect to an equivalent Sobolev inner product. Then the Fourier-like Sobolev orthogonal basis functions are constructed for the diagonalized Laguerre spectral method of elliptic equations. Besides, a unified orthogonal Laguerre projection is established for various elliptic equations. On the basis of this orthogonal Laguerre projection, we obtain optimal error estimates of the fully diagonalized Laguerre spectral method for both Dirichlet and Robin boundary value problems. Finally, numerical experiments, which are in agreement with the theoretical analysis, demonstrate the effectiveness and the spectral accuracy of our diagonalized method.
      PubDate: 2017-03-08
      DOI: 10.1007/s10444-017-9522-3
  • Solving F ( z + 1) = b F(z) in the complex plane
    • Authors: William Paulsen; Samuel Cowgill
      Abstract: Abstract The generalized tetration, defined by the equation F(z+1) = b F(z) in the complex plane with F(0) = 1, is considered for any b > e 1/e . By comparing other solutions to Kneser’s solution, natural conditions are found which force Kneser’s solution to be the unique solution to the equation. This answers a conjecture posed by Trappmann and Kouznetsov. Also, a new iteration method is developed which numerically approximates the function F(z) with an error of less than 10−50 for most bases b, using only 180 nodes, with each iteration gaining one or two places of accuracy. This method can be applied to other problems involving the Abel equation.
      PubDate: 2017-03-07
      DOI: 10.1007/s10444-017-9524-1
  • Improved maximum-norm a posteriori error estimates for linear and
           semilinear parabolic equations
    • Authors: Natalia Kopteva; Torsten Linß
      Abstract: Abstract Linear and semilinear second-order parabolic equations are considered. For these equations, we give a posteriori error estimates in the maximum norm that improve upon recent results in the literature. In particular it is shown that logarithmic dependence on the time step size can be eliminated. Semidiscrete and fully discrete versions of the backward Euler and of the Crank-Nicolson methods are considered. For their full discretizations, we use elliptic reconstructions that are, respectively, piecewise-constant and piecewise-linear in time. Certain bounds for the Green’s function of the parabolic operator are also employed.
      PubDate: 2017-03-02
      DOI: 10.1007/s10444-017-9514-3
  • Construction and analysis of higher order variational integrators for
           dynamical systems with holonomic constraints
    • Authors: Theresa Wenger; Sina Ober-Blöbaum; Sigrid Leyendecker
      Abstract: Abstract In this work, variational integrators of higher order for dynamical systems with holonomic constraints are constructed and analyzed. The construction is based on approximating the configuration and the Lagrange multiplier via different polynomials. The splitting of the augmented Lagrangian in two parts enables the use of different quadrature formulas to approximate the integral of each part. Conditions are derived that ensure the linear independence of the higher order constrained discrete Euler-Lagrange equations and stiff accuracy. Time reversibility is investigated for the discrete flow on configuration level only as for the flow on configuration and momentum level. The fulfillment of the hidden constraints plays an important role for the time reversibility of the presented integrators. The order of convergence is investigated numerically. Order reduction of the momentum and the Lagrange multiplier compared to the order of the configuration occurs in general, but can be avoided by fulfilling the hidden constraints in a simple post processing step. Regarding efficiency versus accuracy a numerical analysis yields that higher orders increase the accuracy of the discrete solution substantially while the computational costs decrease. A comparison to the constrained Galerkin methods in Marsden and West (Acta Numerica 10, 357–514 2001) and the symplectic SPARK integrators of Jay (SIAM Journal on Numerical Analysis 45(5), 1814–1842 2007) reveals that the approach presented here is more general and thus allows for more flexibility in the design of the integrator.
      PubDate: 2017-03-02
      DOI: 10.1007/s10444-017-9520-5
  • Second kind boundary integral equation for multi-subdomain diffusion
    • Authors: X. Claeys; R. Hiptmair; E. Spindler
      Abstract: Abstract We consider isotropic scalar diffusion boundary value problems whose diffusion coefficients are piecewise constant with respect to a partition of space into Lipschitz subdomains. We allow so-called material junctions where three or more subdomains may abut. We derive a boundary integral equation of the second kind posed on the skeleton of the subdomain partition that involves, as unknown, only one trace function at each point of each interface. We prove the well-posedness of the corresponding boundary integral equations. We also report numerical tests for Galerkin boundary element discretisations, in which the new approach proves to be highly competitive compared to the well-established first kind direct single-trace boundary integral formulation. In particular, GMRES seems to enjoy fast convergence independent of the mesh resolution for the discrete second kind BIE.
      PubDate: 2017-03-01
      DOI: 10.1007/s10444-017-9517-0
  • A study of the influence of center conditions on the domain of parameters
           of Newton’s method by using recurrence relations
    • Authors: J. A. Ezquerro; M. A. Hernández-Verón
      Abstract: Abstract This paper focuses on the importance of center conditions on the first derivative of the operator involved in the solution of nonlinear equations by Newton’s method when the semilocal convergence of the method is established from the technique of recurrence relations.
      PubDate: 2017-02-28
      DOI: 10.1007/s10444-017-9518-z
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