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MATHEMATICS (642 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 5)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)

        1 2 3 4 | Last

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  [2341 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)
  • Inverted finite elements for div-curl systems in the whole space
    • Authors: Tahar Z. Boulmezaoud; Keltoum Kaliche; Nabil Kerdid
      Abstract: Abstract We use inverted finite element method (IFEM) for computing three-dimensional vector potentials and for solving div-curl systems in the whole space \(\mathbb {R}^{3}\) . IFEM is substantially different from the existing approaches since it is a non truncature method which preserves the unboundness of the domain. After developping the method, we analyze its convergence in term of weighted norms. We then give some three-dimensional numerical results which demonstrate the efficiency and the accuracy of the method and confirm its convergence.
      PubDate: 2017-04-14
      DOI: 10.1007/s10444-017-9532-1
  • A wirebasket preconditioner for the mortar boundary element method
    • Authors: Thomas Führer; Norbert Heuer
      Abstract: Abstract We present and analyze a preconditioner of the additive Schwarz type for the mortar boundary element method. As a basic splitting, on each subdomain we separate the degrees of freedom related to its boundary from the inner degrees of freedom. The corresponding wirebasket-type space decomposition is stable up to logarithmic terms. For the blocks that correspond to the inner degrees of freedom standard preconditioners for the hypersingular integral operator on open boundaries can be used. For the boundary and interface parts as well as the Lagrangian multiplier space, simple diagonal preconditioners are optimal. Our technique applies to quasi-uniform and non-uniform meshes of shape-regular elements. Numerical experiments on triangular and quadrilateral meshes confirm theoretical bounds for condition and MINRES iteration numbers.
      PubDate: 2017-04-14
      DOI: 10.1007/s10444-017-9534-z
  • Frame completions with prescribed norms: local minimizers and applications
    • Authors: Pedro G. Massey; Noelia B. Rios; Demetrio Stojanoff
      Abstract: Abstract Let \(\mathcal {F}_{0}=\{f_{i}\}_{i\in \mathbb {I}_{n_{0}}}\) be a finite sequence of vectors in \(\mathbb {C}^{d}\) and let \(\mathbf {a}=(a_{i})_{i\in \mathbb {I}_{k}}\) be a finite sequence of positive numbers, where \(\mathbb {I}_{n}=\{1,\ldots , n\}\) for \(n\in \mathbb {N}\) . We consider the completions of \(\mathcal {F}_{0}\) of the form \(\mathcal {F}=(\mathcal {F}_{0},\mathcal {G})\) obtained by appending a sequence \(\mathcal {G}=\{g_{i}\}_{i\in \mathbb {I}_{k}}\) of vectors in \(\mathbb {C}^{d}\) such that ∥g i ∥2 = a i for \(i\in \mathbb {I}_{k}\) , and endow the set of completions with the metric \(d(\mathcal {F},\tilde {\mathcal {F}}) =\max \{ \,\ g_{i}-\tilde {g}_{i}\ : \ i\in \mathbb {I}_{k}\}\) where \(\tilde {\mathcal {F}}=(\mathcal {F}_{0},\,\tilde {\mathcal {G}})\) . In this context we show that local minimizers on the set of completions of a convex potential P φ , induced by a strictly convex function φ, are also global minimizers. In case that φ(x) = x 2 then P φ is the so-called frame potential introduced by Benedetto and Fickus, and our work generalizes several well known results for this potential. We show that there is an intimate connection between frame completion problems with prescribed norms and frame operator distance (FOD) problems. We use this connection and our results to settle in the affirmative a generalized version of Strawn’s conjecture on the FOD.
      PubDate: 2017-04-12
      DOI: 10.1007/s10444-017-9535-y
  • Sparse blind deconvolution and demixing through ℓ 1,2 -minimization
    • Authors: Axel Flinth
      Abstract: Abstract This paper concerns solving the sparse deconvolution and demixing problem using ℓ 1,2-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and Strohmer (Inverse Probl. 31, 115002 2015), and in particular theoretically explain certain experimental findings from that paper. Our results do not only apply to the deconvolution and demixing problem, but to recovery of column-sparse matrices in general.
      PubDate: 2017-04-10
      DOI: 10.1007/s10444-017-9533-0
  • New approximations to the principal real-valued branch of the Lambert W
    • Authors: Roberto Iacono; John P. Boyd
      Abstract: Abstract The Lambert W-function is the solution to the transcendental equation W(x)e W(x) = x. It has two real branches, one of which, for x ∈ [−1/e, ∞], is usually denoted as the principal branch. On this branch, the function grows from − 1 to infinity, logarithmically at large x. The present work is devoted to the construction of accurate approximations for the principal branch of the W-function. In particular, a simple, global analytic approximation is derived that covers the whole branch with a maximum relative error smaller than 5 × 10−3. Starting from it, machine precision accuracy is reached everywhere with only three steps of a quadratically convergent iterative scheme, here examined for the first time, which is more efficient than standard Newton’s iteration at large x. Analytic bounds for W are also constructed, for x > e, which are much tighter than those currently available. It is noted that the exponential of the upper bounding function yields an upper bound for the prime counting function π(n) that is better than the well-known Chebyshev’s estimates at large n. Finally, the construction of accurate approximations to W based on Chebyshev spectral theory is discussed; the difficulties involved are highlighted, and methods to overcome them are presented.
      PubDate: 2017-04-01
      DOI: 10.1007/s10444-017-9530-3
  • An h - p version of the continuous Petrov-Galerkin method for Volterra
           delay-integro-differential equations
    • Authors: Lina Wang; Lijun Yi
      Abstract: Abstract We consider an h-p version of the continuous Petrov-Galerkin time stepping method for Volterra integro-differential equations with proportional delays. We derive a priori error bounds in the L 2-, H 1- and L ∞-norm that are explicit in the local time steps, the local approximation orders, and the local regularity of the exact solution. Numerical experiments are presented to illustrate the theoretical results.
      PubDate: 2017-03-27
      DOI: 10.1007/s10444-017-9531-2
  • 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
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