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MATHEMATICS (715 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: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 29)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
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: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
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: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 6)
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: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
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: 5)
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: 4)
Annals of Data Science     Hybrid Journal   (Followers: 12)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
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)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
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: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
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: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
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: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
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: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
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: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
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: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
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: 5)
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: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
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: 29)
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: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
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: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)

        1 2 3 4 | Last

Journal Cover
Advances in Computational Mathematics
Journal Prestige (SJR): 0.812
Citation Impact (citeScore): 1
Number of Followers: 19  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9044 - ISSN (Online) 1019-7168
Published by Springer-Verlag Homepage  [2351 journals]
  • Two scale Hardy space infinite elements for scalar waveguide problems
    • Authors: Martin Halla; Lothar Nannen
      Pages: 611 - 643
      Abstract: We consider the numerical solution of the Helmholtz equation in domains with one infinite cylindrical waveguide. Such problems exhibit wavenumbers on different scales in the vicinity of cut-off frequencies. This leads to performance issues for non-modal methods like the perfectly matched layer or the Hardy space infinite element method. To improve the latter, we propose a two scale Hardy space infinite element method which can be optimized for wavenumbers on two different scales. It is a tensor product Galerkin method and fits into existing analysis. Up to arbitrary small thresholds it converges exponentially with respect to the number of longitudinal unknowns in the waveguide. Numerical experiments support the theoretical error bounds.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9549-5
      Issue No: Vol. 44, No. 3 (2018)
  • Scattered data fitting of Hermite type by a weighted meshless method
    • Authors: M. Esmaeilbeigi; O. Chatrabgoun; M. Shafa
      Pages: 673 - 691
      Abstract: In many practical problems, it is often desirable to interpolate not only the function values but also the values of derivatives up to certain order, as in the Hermite interpolation. The Hermite interpolation method by radial basis functions is used widely for solving scattered Hermite data approximation problems. However, sometimes it makes more sense to approximate the solution by a least squares fit. This is particularly true when the data are contaminated with noise. In this paper, a weighted meshless method is presented to solve least squares problems with noise. The weighted meshless method by Gaussian radial basis functions is proposed to fit scattered Hermite data with noise in certain local regions of the problem’s domain. Existence and uniqueness of the solution is proved. This approach has one parameter which can adjust the accuracy according to the size of the noise. Another advantage of the weighted meshless method is that it can be used for problems in high dimensions with nonregular domains. The numerical experiments show that our weighted meshless method has better performance than the traditional least squares method in the case of noisy Hermite data.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9555-7
      Issue No: Vol. 44, No. 3 (2018)
  • On numerical density approximations of solutions of SDEs with unbounded
    • Authors: Linghua Chen; Espen Robstad Jakobsen; Arvid Naess
      Pages: 693 - 721
      Abstract: We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in application oriented fields. In this paper we provide a rigorous analysis of the method that covers systems of equations with unbounded coefficients. Working in a natural space for densities, L 1, we obtain stability, consistency, and new convergence results for the method, new well-posedness and semigroup generation results for the related Fokker-Planck-Kolmogorov equation, and a new and rigorous connection to the corresponding probability density functions for both the approximate and the exact problems. To prove the results we combine semigroup and PDE arguments in a new way that should be of independent interest.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9558-4
      Issue No: Vol. 44, No. 3 (2018)
  • Alternating direction method of multipliers with difference of convex
    • Authors: Tao Sun; Penghang Yin; Lizhi Cheng; Hao Jiang
      Pages: 723 - 744
      Abstract: In this paper, we consider the minimization of a class of nonconvex composite functions with difference of convex structure under linear constraints. While this kind of problems in theory can be solved by the celebrated alternating direction method of multipliers (ADMM), a direct application of ADMM often leads to difficult nonconvex subproblems. To address this issue, we propose to convexify the subproblems through a linearization technique as done in the difference of convex functions algorithm (DCA). By assuming the Kurdyka-Łojasiewicz property, we prove that the resulting algorithm sequentially converges to a critical point. It turns out that in the applications of signal and image processing such as compressed sensing and image denoising, the proposed algorithm usually enjoys closed-form solutions of the subproblems and thus can be very efficient. We provide numerical experiments to demonstrate the effectiveness of our algorithm.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9559-3
      Issue No: Vol. 44, No. 3 (2018)
  • Adaptive energy preserving methods for partial differential equations
    • Authors: Sølve Eidnes; Brynjulf Owren; Torbjørn Ringholm
      Pages: 815 - 839
      Abstract: A framework for constructing integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The approach can be used with both finite difference and partition of unity methods, thereby including finite element methods. The schemes are then extended to accommodate r-, h- and p-adaptivity. To illustrate the ideas, the method is applied to the Korteweg–de Vries equation and the sine-Gordon equation. Results from numerical experiments are presented.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9562-8
      Issue No: Vol. 44, No. 3 (2018)
  • High-precision computation of the confluent hypergeometric functions via
           Franklin-Friedman expansion
    • Authors: Guillermo Navas-Palencia
      Pages: 841 - 859
      Abstract: We present a method of high-precision computation of the confluent hypergeometric functions using an effective computational approach of what we termed Franklin-Friedman expansions. These expansions are convergent under mild conditions of the involved amplitude function and for some interesting cases the coefficients can be rapidly computed, thus providing a viable alternative to the conventional dichotomy between series expansion and asymptotic expansion. The present method has been extensively tested in different regimes of the parameters and compared with recently investigated convergent and uniform asymptotic expansions.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9565-5
      Issue No: Vol. 44, No. 3 (2018)
  • The spectral collocation method for efficiently solving PDEs with
           fractional Laplacian
    • Authors: Hong Lu; Peter W. Bates; Wenping Chen; Mingji Zhang
      Pages: 861 - 878
      Abstract: We derive a spectral collocation approximation to the fractional Laplacian operator based on the Riemann-Liouville fractional derivative operators on a bounded domain Ω = [a, b]. Corresponding matrix representations of (−△) α/2 for α ∈ (0,1) and α ∈ (1,2) are obtained. A space-fractional advection-dispersion equation is then solved to investigate the numerical performance of this method under various choices of parameters. It turns out that the proposed method has high accuracy and is efficient for solving these space-fractional advection-dispersion equations when the forcing term is smooth.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9564-6
      Issue No: Vol. 44, No. 3 (2018)
  • Real phase retrieval from unordered partial frame coefficients
    • Authors: Fusheng Lv; Wenchang Sun
      Pages: 879 - 896
      Abstract: We study the signal recovery from unordered partial phaseless frame coefficients. To this end, we introduce the concepts of m-erasure (almost) phase retrievable frames. We show that with an m-erasure (almost) phase retrievable frame, it is possible to reconstruct (almost) all n-dimensional real signals up to a sign from their arbitrary N − m unordered phaseless frame coefficients, where N stands for the element number of the frame. We give necessary and sufficient conditions for a frame to be m-erasure (almost) phase retrievable. Moreover, we give an explicit construction of such frames based on prime numbers.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9566-4
      Issue No: Vol. 44, No. 3 (2018)
  • Coercivity results of a modified Q 1 -finite volume element scheme for
           anisotropic diffusion problems
    • Authors: Qi Hong; Jiming Wu
      Pages: 897 - 922
      Abstract: In this paper, we study a so-called modified Q 1-finite volume element scheme that is obtained by employing the trapezoidal rule to approximate the line integrals in the classical Q 1-finite volume element method. A necessary and sufficient condition is obtained for the positive definiteness of a certain element stiffness matrix. Based on this result, a sufficient condition is suggested to guarantee the coercivity of the scheme on arbitrary convex quadrilateral meshes. When the diffusion tensor is an identity matrix, this sufficient condition reduces to a geometric one, covering some standard meshes, such as the traditional h 1+γ -parallelogram meshes and some trapezoidal meshes. More interesting is that, this sufficient condition has explicit expression, by which one can easily judge on any diffusion tensor and any mesh with any mesh size h > 0. The H 1 error estimate of the modified Q 1-finite volume element scheme is obtained without the traditional h 1+γ -parallelogram assumption. Some numerical experiments are carried out to validate the theoretical analysis.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9567-3
      Issue No: Vol. 44, No. 3 (2018)
  • Analysis of linearized Galerkin-mixed FEMs for the time-dependent
           Ginzburg-Landau equations of superconductivity
    • Authors: Huadong Gao; Weiwei Sun
      Pages: 923 - 949
      Abstract: A linearized backward Euler Galerkin-mixed finite element method is investigated for the time-dependent Ginzburg-Landau (TDGL) equations under the Lorentz gauge. By introducing the induced magnetic field σ = c u r l A as a new variable, the Galerkin-mixed FE scheme offers many advantages over conventional Lagrange type Galerkin FEMs. An optimal error estimate for the linearized Galerkin-mixed FE scheme is established unconditionally. Analysis is given under more general assumptions for the regularity of the solution of the TDGL equations, which includes the problem in two-dimensional nonconvex polygons and certain three dimensional polyhedrons, while the conventional Galerkin FEMs may not converge to a true solution in these cases. Numerical examples in both two and three dimensional spaces are presented to confirm our theoretical analysis. Numerical results show clearly the efficiency of the mixed method, particularly for problems on nonconvex domains.
      PubDate: 2018-06-01
      DOI: 10.1007/s10444-017-9568-2
      Issue No: Vol. 44, No. 3 (2018)
  • Adaptive refinement for hp –Version Trefftz discontinuous Galerkin
           methods for the homogeneous Helmholtz problem
    • Authors: Scott Congreve; Paul Houston; Ilaria Perugia
      Abstract: In this article, we develop an hp-adaptive refinement procedure for Trefftz discontinuous Galerkin methods applied to the homogeneous Helmholtz problem. Our approach combines not only mesh subdivision (h–refinement) and local basis enrichment (p–refinement), but also incorporates local directional adaptivity, whereby the elementwise plane wave basis is aligned with the dominant scattering direction. Numerical experiments based on employing an empirical a posteriori error indicator clearly highlight the efficiency of the proposed approach for various examples.
      PubDate: 2018-07-16
      DOI: 10.1007/s10444-018-9621-9
  • Randomized algorithms for the approximations of Tucker and the tensor
           train decompositions
    • Authors: Maolin Che; Yimin Wei
      Abstract: Randomized algorithms provide a powerful tool for scientific computing. Compared with standard deterministic algorithms, randomized algorithms are often faster and robust. The main purpose of this paper is to design adaptive randomized algorithms for computing the approximate tensor decompositions. We give an adaptive randomized algorithm for the computation of a low multilinear rank approximation of the tensors with unknown multilinear rank and analyze its probabilistic error bound under certain assumptions. Finally, we design an adaptive randomized algorithm for computing the tensor train approximations of the tensors. Based on the bounds about the singular values of sub-Gaussian matrices with independent columns or independent rows, we analyze these randomized algorithms. We illustrate our adaptive randomized algorithms via several numerical examples.
      PubDate: 2018-07-05
      DOI: 10.1007/s10444-018-9622-8
  • POD reduced-order modeling for evolution equations utilizing arbitrary
           finite element discretizations
    • Authors: Carmen Gräßle; Michael Hinze
      Abstract: The main focus of the present work is the inclusion of spatial adaptivity for the snapshot computation in the offline phase of model order reduction utilizing proper orthogonal decomposition (POD-MOR) for nonlinear parabolic evolution problems. We consider snapshots which live in different finite element spaces, which means in a fully discrete setting that the snapshots are vectors of different length. From a numerical point of view, this leads to the problem that the usual POD procedure which utilizes a singular value decomposition of the snapshot matrix, cannot be carried out. In order to overcome this problem, we here construct the POD model/basis using the eigensystem of the correlation matrix (snapshot Gramian), which is motivated from a continuous perspective and is set up explicitly, e.g., without the necessity of interpolating snapshots into a common finite element space. It is an advantage of this approach that the assembly of the matrix only requires the evaluation of inner products of snapshots in a common Hilbert space. This allows a great flexibility concerning the spatial discretization of the snapshots. The analysis for the error between the resulting POD solution and the true solution reveals that the accuracy of the reduced-order solution can be estimated by the spatial and temporal discretization error as well as the POD error. Finally, to illustrate the feasibility of our approach, we present a test case of the Cahn–Hilliard system utilizing h-adapted hierarchical meshes and two settings of a linear heat equation using nested and non-nested grids.
      PubDate: 2018-06-27
      DOI: 10.1007/s10444-018-9620-x
  • ADMM for monotone operators: convergence analysis and rates
    • Authors: Radu Ioan Boţ; Ernö Robert Csetnek
      Abstract: We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We show that a number of primal-dual algorithms for monotone inclusions and also the classical ADMM numerical scheme for convex optimization problems, along with some of its variants, can be embedded in this unifying scheme. While in the first part of the paper, convergence results for the iterates are reported, the second part is devoted to the derivation of convergence rates obtained by combining variable metric techniques with strategies based on suitable choice of dynamical step sizes. The numerical performances, which can be obtained for different dynamical step size strategies, are compared in the context of solving an image denoising problem.
      PubDate: 2018-06-25
      DOI: 10.1007/s10444-018-9619-3
  • A Ljusternik-Schnirelman minimax algorithm for finding equality
           constrained saddle points and its application for solving Eigen problems:
           part I. Algorithm and global convergence
    • Authors: Xudong Yao
      Abstract: In Yao (J. Sci. Comput. 66, 19–40 2016), two Ljusternik-Schnirelman minimax algorithms for capturing multiple free saddle points are developed from well-known Ljusternik-Schnirelman critical point theory, numerical experiment is carried out and global convergence is established. In this paper, a Ljusternik-Schnirelman minimax algorithm for calculating multiple equality constrained saddle points is presented. The algorithm is applied to numerically solve eigen problems. Finally, global convergence for the algorithm is verified.
      PubDate: 2018-06-22
      DOI: 10.1007/s10444-018-9616-6
  • Clustering approach to model order reduction of power networks with
           distributed controllers
    • Authors: Xiaodong Cheng; Jacquelien M. A. Scherpen
      Abstract: This paper considers the network structure preserving model reduction of power networks with distributed controllers. The studied system and controller are modeled as second-order and first-order ordinary differential equations, which are coupled to a closed-loop model for analyzing the dissimilarities of the power units. By transfer functions, we characterize the behavior of each node (generator or load) in the power network and define a novel notion of dissimilarity between two nodes by the \(\mathcal {H}_{2}\) -norm of the transfer function deviation. Then, the reduction methodology is developed based on separately clustering the generators and loads according to their behavior dissimilarities. The characteristic matrix of the resulting clustering is adopted for the Galerkin projection to derive explicit reduced-order power models and controllers. Finally, we illustrate the proposed method by the IEEE 30-bus system example.
      PubDate: 2018-06-16
      DOI: 10.1007/s10444-018-9617-5
  • On a correction of a property of GC n sets
    • Authors: Hakop Hakopian; Vahagn Vardanyan
      Abstract: An n-poised node set \(\mathcal {X}\) in the plane is called GC n set if the (bivariate) fundamental polynomial of each node is a product of n linear factors. A line is called k-node line if it passes through exactly k-nodes of \(\mathcal {X}\) . An (n + 1)-node line is called a maximal line. In 1982, Gasca and Maeztu conjectured that every GC n set has a maximal line. Until now the conjecture has been proved only for n ≤ 5. We say that a node uses a line if the line is a factor of the fundamental polynomial of this node. It is a simple fact that any maximal line λ is used by all \(\binom {n + 1}{2}\) nodes in \(\mathcal {X} \setminus \lambda \) . We consider the main result of the paper—Bayramyan and Hakopian (Adv. Comput. Math. 43, 607–626, 2017) stating that any n-node line of GC n set is used either by exactly \(\binom {n}{2}\) nodes or by exactly \(\binom {n-1}{2}\) nodes, provided that the Gasca-Maeztu conjecture is true. Here, we show that this result is not correct in the case n = 3. Namely, we bring an example of a GC3 set and a 3-node line there which is not used at all. Fortunately, then we were able to establish that this is the only possible counterexample, i.e., the abovementioned result is true for all n ≥ 4. We also characterize the exclusive case n = 3 and present some new results on the maximal lines and the usage of n-node lines in GC n sets.
      PubDate: 2018-06-12
      DOI: 10.1007/s10444-018-9618-4
  • Balanced truncation model order reduction in limited time intervals for
           large systems
    • Authors: Patrick Kürschner
      Abstract: In this article we investigate model order reduction of large-scale systems using time-limited balanced truncation, which restricts the well known balanced truncation framework to prescribed finite time intervals. The main emphasis is on the efficient numerical realization of this model reduction approach in case of large system dimensions. We discuss numerical methods to deal with the resulting matrix exponential functions and Lyapunov equations which are solved for low-rank approximations. Our main tool for this purpose are rational Krylov subspace methods. We also discuss the eigenvalue decay and numerical rank of the solutions of the Lyapunov equations. These results, and also numerical experiments, will show that depending on the final time horizon, the numerical rank of the Lyapunov solutions in time-limited balanced truncation can be smaller compared to standard balanced truncation. In numerical experiments we test the approaches for computing low-rank factors of the involved Lyapunov solutions and illustrate that time-limited balanced truncation can generate reduced order models having a higher accuracy in the considered time region.
      PubDate: 2018-06-05
      DOI: 10.1007/s10444-018-9608-6
  • Elementary factorisation of Box spline subdivision
    • Authors: Cédric Gérot
      Abstract: When a subdivision scheme is factorised into lifting steps, it admits an in–place and invertible implementation, and it can be the predictor of many multiresolution biorthogonal wavelet transforms. In the regular setting where the underlying lattice hierarchy is defined by ℤ s and a dilation matrix M, such a factorisation should deal with every vertex of each subset in ℤ s /Mℤ s in the same way. We define a subdivision scheme which admits such a factorisation as being uniformly elementary factorable. We prove a necessary and sufficient condition on the directions of the Box spline and the arity of the subdivision for the scheme to admit such a factorisation, and recall some known keys to construct it in practice.
      PubDate: 2018-06-05
      DOI: 10.1007/s10444-018-9612-x
  • Tetration for complex bases
    • Authors: William Paulsen
      Abstract: In this paper we will consider the tetration, defined by the equation F(z + 1) = bF(z) in the complex plane with F(0) = 1, for the case where b is complex. A previous paper determined conditions for a unique solution the case where b is real and b > e1/e. In this paper we extend these results to find conditions which determine a unique solution for complex bases. We also develop iteration methods for numerically approximating the function F(z), both for bases inside and outside the Shell-Thron region.
      PubDate: 2018-06-02
      DOI: 10.1007/s10444-018-9615-7
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