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MATHEMATICS (645 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
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: 4)
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 Network Science     Open Access  
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: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
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)

        1 2 3 4 | Last

Journal Cover BIT Numerical Mathematics
  [SJR: 1.221]   [H-I: 40]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1572-9125 - ISSN (Online) 0006-3835
   Published by Springer-Verlag Homepage  [2329 journals]
  • Modified Douglas splitting methods for reaction–diffusion equations
    • Authors: A. Arrarás; K. J. in ’t Hout; W. Hundsdorfer; L. Portero
      Pages: 261 - 285
      Abstract: We present modifications of the second-order Douglas stabilizing corrections method, which is a splitting method based on the implicit trapezoidal rule. Inclusion of an explicit term in a forward Euler way is straightforward, but this will lower the order of convergence. In the modifications considered here, explicit terms are included in a second-order fashion. For these modified methods, results on linear stability and convergence are derived. Stability holds for important classes of reaction–diffusion equations, and for such problems the modified Douglas methods are seen to be often more efficient than related methods from the literature.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0634-9
      Issue No: Vol. 57, No. 2 (2017)
  • Regularized HSS iteration methods for saddle-point linear systems
    • Authors: Zhong-Zhi Bai; Michele Benzi
      Pages: 287 - 311
      Abstract: We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspace methods. We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding preconditioned matrix. Inexact variants are also considered. Numerical results on saddle-point linear systems arising from the discretization of a Stokes problem and of a distributed control problem show that good performance can be achieved when using inexact variants of the proposed preconditioners.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0636-7
      Issue No: Vol. 57, No. 2 (2017)
  • A G-symplectic method with order 6
    • Authors: John C. Butcher; Gulshad Imran; Helmut Podhaisky
      Pages: 313 - 328
      Abstract: G-symplectic methods are an alternative to symplectic Runge–Kutta in that they have similar numerical behaviour but are less expensive computationally. In this paper, a new method is derived which is symmetric, G-symplectic, has zero parasitic growth factors and has order 6. Although there are five stages, two of these are explicit and the remaining three are diagonally implicit. The method is multivalue, with four quantities passed from step to step. No drift in the variation of the Hamiltonian is observed in numerical experiments for long time intervals if the stepsize is sufficiently small.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0630-0
      Issue No: Vol. 57, No. 2 (2017)
  • Quasi-interpolation based on the ZP-element for the numerical solution of
           integral equations on surfaces in $$\mathbb {R}^3$$ R 3
    • Authors: Catterina Dagnino; Sara Remogna
      Pages: 329 - 350
      Abstract: The aim of this paper is to present spline methods for the numerical solution of integral equations on surfaces of \(\mathbb {R}^3\) , by using optimal superconvergent quasi-interpolants defined on type-2 triangulations and based on the Zwart–Powell quadratic box spline. In particular we propose a modified version of the classical collocation method and two spline collocation methods with high order of convergence. We also deal with the problem of approximating the surface. Finally, we study the approximation error of the above methods together with their iterated versions and we provide some numerical tests.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0633-x
      Issue No: Vol. 57, No. 2 (2017)
  • Majorization–minimization generalized Krylov subspace methods for
           $${\ell _p}$$ ℓ p – $${\ell _q}$$ ℓ q optimization applied to image
    • Authors: G. Huang; A. Lanza; S. Morigi; L. Reichel; F. Sgallari
      Pages: 351 - 378
      Abstract: A new majorization–minimization framework for \(\ell _p\) – \(\ell _q\) image restoration is presented. The solution is sought in a generalized Krylov subspace that is build up during the solution process. Proof of convergence to a stationary point of the minimized \(\ell _p\) – \(\ell _q\) functional is provided for both convex and nonconvex problems. Computed examples illustrate that high-quality restorations can be determined with a modest number of iterations and that the storage requirement of the method is not very large. A comparison with related methods shows the competitiveness of the method proposed.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0643-8
      Issue No: Vol. 57, No. 2 (2017)
  • A breakdown-free block conjugate gradient method
    • Authors: Hao Ji; Yaohang Li
      Pages: 379 - 403
      Abstract: In this paper, we analyze all possible situations of rank deficiency that cause breakdown in block conjugate gradient (BCG) solvers. A simple solution, breakdown-free block conjugate gradient (BFBCG), is designed to address the rank deficiency problem. The rationale of the BFBCG algorithm is to derive new forms of parameter matrices based on the potentially reduced search subspace to handle rank deficiency. Orthogonality properties and convergence of BFBCG in case of rank deficiency are justified accordingly with mathematical rigor. BFBCG yields faster convergence than restarting BCG when breakdown occurs. Numerical examples suffering from rank deficiency are provided to demonstrate the robustness of BFBCG.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0631-z
      Issue No: Vol. 57, No. 2 (2017)
  • Robust preconditioners for PDE-constrained optimization with limited
    • Authors: Kent-André Mardal; Bjørn Fredrik Nielsen; Magne Nordaas
      Pages: 405 - 431
      Abstract: Regularization robust preconditioners for PDE-constrained optimization problems have been successfully developed. These methods, however, typically assume observation data and control throughout the entire domain of the state equation. For many inverse problems, this is an unrealistic assumption. In this paper we propose and analyze preconditioners for PDE-constrained optimization problems with limited observation data, e.g. observations are only available at the boundary of the solution domain. Our methods are robust with respect to both the regularization parameter and the mesh size. That is, the condition number of the preconditioned optimality system is uniformly bounded, independently of the size of these two parameters. The method does, however, require extra regularity. We first consider a prototypical elliptic control problem and thereafter more general PDE-constrained optimization problems. Our theoretical findings are illuminated by several numerical results.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0635-8
      Issue No: Vol. 57, No. 2 (2017)
  • Structural analysis based dummy derivative selection for differential
           algebraic equations
    • Authors: Ross McKenzie; John Pryce
      Pages: 433 - 462
      Abstract: The signature matrix structural analysis method developed by Pryce provides more structural information than the commonly used Pantelides method and applies to differential-algebraic equations (DAEs) of arbitrary order. It is useful to consider how existing methods using the Pantelides algorithm can benefit from such structural analysis. The dummy derivative method is a technique commonly used to solve DAEs that can benefit from such exploitation of underlying DAE structures and information found in the Signature Matrix method. This paper gives a technique to find structurally necessary dummy derivatives and how to use different block triangular forms effectively when performing the dummy derivative method and then provides a brief complexity analysis of the proposed approach. We finish by outlining an approach that can simplify the task of dummy pivoting.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0642-9
      Issue No: Vol. 57, No. 2 (2017)
  • Invariant curves for the discretised van der Pol equation
    • Authors: Kaspar Nipp; Daniel Stoffer
      Pages: 463 - 497
      Abstract: It is well known that the stiff van der Pol equation has a strongly attractive limit cycle. In this paper it is shown that the Euler method applied to the van der Pol equation with small step size, small compared to the perturbation parameter, admits an attractive invariant closed curve close to the limit cycle. To describe closed curves in the vicinity of the limit cycle, 14 charts are introduced. A general graph transform result is derived and applied in these charts. The proof of the main result relies on the contraction principle in a suitable function space. Estimates are given for the distance of the invariant curve to the limit cycle.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0638-5
      Issue No: Vol. 57, No. 2 (2017)
  • Efficient estimation of regularization parameters via downsampling and the
           singular value expansion
    • Authors: Rosemary A. Renaut; Michael Horst; Yang Wang; Douglas Cochran; Jakob Hansen
      Pages: 499 - 529
      Abstract: The solution, \(\varvec{x}\) , of the linear system of equations \(A\varvec{x}\approx \varvec{b}\) arising from the discretization of an ill-posed integral equation \(g(s)=\int H(s,t) f(t) \,dt\) with a square integrable kernel H(s, t) is considered. The Tikhonov regularized solution \(\varvec{x}(\lambda )\) approximating the Galerkin coefficients of f(t) is found as the minimizer of \(J(\varvec{x})=\{ \Vert A \varvec{x} -\varvec{b}\Vert _2^2 + \lambda ^2 \Vert L \varvec{x}\Vert _2^2\}\) , where \(\varvec{b}\) is given by the Galerkin coefficients of g(s). \(\varvec{x}(\lambda )\) depends on the regularization parameter \(\lambda \) that trades off between the data fidelity and the smoothing norm determined by L, here assumed to be diagonal and invertible. The Galerkin method provides the relationship between the singular value expansion of the continuous kernel and the singular value decomposition of the discrete system matrix for square integrable kernels. We prove that the kernel maintains square integrability under left and right multiplication by bounded functions and thus the relationship also extends to appropriately weighted kernels. The resulting approximation of the integral equation permits examination of the properties of the regularized solution \(\varvec{x}(\lambda )\) independent of the sample size of the data. We prove that consistently down sampling both the system matrix and the data provides a small scale system that preserves the dominant terms of the right singular subspace of the system and can then be used to estimate the regularization parameter for the original system. When g(s) is directly measured via its Galerkin coefficients the regularization parameter is preserved across resolutions. For measurements of g(s) a scaling argument is required to move across resolutions of the systems when the regularization parameter is found using a regularization parameter estimation technique that depends on the knowledge of the variance in the data. Numerical results illustrate the theory and demonstrate the practicality of the approach for regularization parameter estimation using generalized cross validation, unbiased predictive risk estimation and the discrepancy principle applied to both the system of equations, and to the regularized system of equations.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0637-6
      Issue No: Vol. 57, No. 2 (2017)
  • Interval unions
    • Authors: Hermann Schichl; Ferenc Domes; Tiago Montanher; Kevin Kofler
      Pages: 531 - 556
      Abstract: This paper introduces interval union arithmetic, a new concept which extends the traditional interval arithmetic. Interval unions allow to manipulate sets of disjoint intervals and provide a natural way to represent the extended interval division. Considering interval unions lead to simplifications of the interval Newton method as well as of other algorithms for solving interval linear systems. This paper does not aim at describing the complete theory of interval union analysis, but rather at giving basic definitions and some fundamental properties, as well as showing theoretical and practical usefulness of interval unions in a few selected areas.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0632-y
      Issue No: Vol. 57, No. 2 (2017)
  • Sharp mean-square regularity results for SPDEs with fractional noise and
           optimal convergence rates for the numerical approximations
    • Authors: Xiaojie Wang; Ruisheng Qi; Fengze Jiang
      Pages: 557 - 585
      Abstract: This article offers sharp spatial and temporal mean-square regularity results for a class of semi-linear parabolic stochastic partial differential equations (SPDEs) driven by infinite dimensional fractional Brownian motion with the Hurst parameter greater than one-half. In addition, the mean-square numerical approximations of such problems are investigated, performed by the spectral Galerkin method in space and the linear implicit Euler method in time. The obtained sharp regularity properties of the problems enable us to identify optimal mean-square convergence rates of the full discrete scheme. These theoretical findings are accompanied by several numerical examples.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0639-4
      Issue No: Vol. 57, No. 2 (2017)
  • Linearly implicit BDF methods for nonlinear parabolic interface problems
    • Authors: Chaoxia Yang
      Pages: 587 - 606
      Abstract: We analyze linearly implicit BDF methods for the time discretization of a nonlinear parabolic interface problem, where the computational domain is divided into two subdomains by an interface, and the nonlinear diffusion coefficient is discontinuous across the interface. We prove optimal-order error estimates without assuming any growth conditions on the nonlinear diffusion coefficient and without restriction on the stepsize. Due to the existence of the interface and the lack of global Lipschitz continuity of the diffusion coefficient, we use a special type of test functions to analyze high-order \(A(\alpha )\) -stable BDF methods. Such test functions avoid any interface terms upon integration by parts and are used to derive error estimates in the piecewise \(H^2\) norm.
      PubDate: 2017-06-01
      DOI: 10.1007/s10543-016-0641-x
      Issue No: Vol. 57, No. 2 (2017)
  • GCV for Tikhonov regularization by partial SVD
    • Authors: Caterina Fenu; Lothar Reichel; Giuseppe Rodriguez; Hassane Sadok
      Abstract: Tikhonov regularization is commonly used for the solution of linear discrete ill-posed problems with error-contaminated data. A regularization parameter that determines the quality of the computed solution has to be chosen. One of the most popular approaches to choosing this parameter is to minimize the Generalized Cross Validation (GCV) function. The minimum can be determined quite inexpensively when the matrix A that defines the linear discrete ill-posed problem is small enough to rapidly compute its singular value decomposition (SVD). We are interested in the solution of linear discrete ill-posed problems with a matrix A that is too large to make the computation of its complete SVD feasible, and show how upper and lower bounds for the numerator and denominator of the GCV function can be determined fairly inexpensively for large matrices A by computing only a few of the largest singular values and associated singular vectors of A. These bounds are used to determine a suitable value of the regularization parameter. Computed examples illustrate the performance of the proposed method.
      PubDate: 2017-05-18
      DOI: 10.1007/s10543-017-0662-0
  • On the structured backward error of inexact Arnoldi methods for
           (skew)-Hermitian and (skew)-symmetric eigenvalue problems
    • Authors: Ching-Sung Liu; Che-Rung Lee
      Abstract: In this paper, we present the inexact structure preserving Arnoldi methods for structured eigenvalue problems. They are called structure preserving because the computed eigenvalues and eigenvectors can preserve the desirable properties of the structures of the original matrices, even with large errors involved in the computation of matrix-vector products. A backward error matrix is called structured if it has the same structure as the original matrix. We derive a common form for the structured backward errors that can be used for different structure preserving processes, and prove the derived form has the minimum Frobenius norm among all possible backward errors. Furthermore, we employ the derived backward errors for some specific structure preserving processes to estimate the accuracy of the solutions obtained by inexact Arnoldi methods for eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to compute so that they can be used routinely in practice. Numerical experiments are provided to support the theoretical results.
      PubDate: 2017-05-08
      DOI: 10.1007/s10543-017-0660-2
  • Pointwise estimates of SDFEM on Shishkin triangular meshes for problems
           with exponential layers
    • Authors: Jin Zhang; Xiaowei Liu
      Abstract: In this paper, we present a pointwise convergence analysis for a streamline diffusion finite element method (SDFEM) on a Shishkin triangular mesh. We prove that the method is uniformly convergent with a pointwise accuracy of order almost 7/4 (up to a logarithmic factor) away from the subdomain where the layers intersect. Finally, numerical experiments support our theoretical results.
      PubDate: 2017-05-08
      DOI: 10.1007/s10543-017-0661-1
  • Direct approximation on spheres using generalized moving least squares
    • Authors: Davoud Mirzaei
      Abstract: In this paper a direct approximation method on the sphere, constructed by generalized moving least squares, is presented and analyzed. It is motivated by numerical solution of partial differential equations on spheres and other manifolds. The new method generalizes the finite difference methods, someway, for scattered data points on each local subdomain. As an application, the Laplace–Beltrami equation is solved and the theoretical and experimental results are given. The new approach eliminates some drawbacks of the previous methods.
      PubDate: 2017-05-03
      DOI: 10.1007/s10543-017-0659-8
  • Error estimates for the summation of real numbers with application to
           floating-point summation
    • Authors: Marko Lange; Siegfried M. Rump
      Abstract: Standard Wilkinson-type error estimates of floating-point algorithms involve a factor \(\gamma _k:=k\mathbf {u}/(1-k\mathbf {u})\) for \(\mathbf {u}\) denoting the relative rounding error unit of a floating-point number system. Recently, it was shown that, for many standard algorithms such as matrix multiplication, LU- or Cholesky decomposition, \(\gamma _k\) can be replaced by \(k\mathbf {u}\) , and the restriction on k can be removed. However, the arguments make heavy use of specific properties of both the underlying set of floating-point numbers and the corresponding arithmetic. In this paper, we derive error estimates for the summation of real numbers where each sum is afflicted with some perturbation. Recent results on floating-point summation follow as a corollary, in particular error estimates for rounding to nearest and for directed rounding. Our new estimates are sharp and unveil the necessary properties of floating-point schemes to allow for a priori estimates of summation with a factor omitting higher order terms.
      PubDate: 2017-05-03
      DOI: 10.1007/s10543-017-0658-9
  • Using interval unions to solve linear systems of equations with
    • Authors: Tiago Montanher; Ferenc Domes; Hermann Schichl; Arnold Neumaier
      Abstract: An interval union is a finite set of closed and disjoint intervals. In this paper we introduce the interval union Gauss–Seidel procedure to rigorously enclose the solution set of linear systems with uncertainties given by intervals or interval unions. We also present the interval union midpoint and Gauss–Jordan preconditioners. The Gauss–Jordan preconditioner is used in a mixed strategy to improve the quality and efficiency of the algorithm. Numerical experiments on interval linear systems generated at random show the capabilities of our approach.
      PubDate: 2017-04-22
      DOI: 10.1007/s10543-017-0657-x
  • Symbols and exact regularity of symmetric pseudo-splines of any arity
    • Authors: Georg Muntingh
      Abstract: Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc–Deslauriers schemes and B-spline schemes. Using a generating function approach, we derive expressions for the symbols of the symmetric m-ary pseudo-spline subdivision schemes. We show that their masks have positive Fourier transform, making it possible to compute the exact Hölder regularity algebraically as a logarithm of the spectral radius of a matrix. We apply this method to compute the regularity explicitly in some special cases, including the symmetric binary, ternary, and quarternary pseudo-spline schemes.
      PubDate: 2017-04-13
      DOI: 10.1007/s10543-017-0656-y
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