A tridiagonalization-based arbitrary-stride reduction approach for (p,q)-pentadiagonal linear systems: A tridiagonalization-based arbitrary-stride reduction approach for \((p,q)\)-pentadiagonal linear systems

Authors: Yi-Fan Wang, Ji-Teng Jia, Xin Fan

Source: Applied Numerical Mathematics. 213:77-87

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, \((p, q)\)-pentadiagonal matrix, Diagonalization, Jordan forms, arbitrary-stride reduction, tridiagonalization, extended condition number, linear system, Direct numerical methods for linear systems and matrix inversion, condition number

File Description: application/xml

Access URL: https://zbmath.org/8034918
https://doi.org/10.1016/j.apnum.2025.02.017

Fast and accurate recursive algorithms for solving cyclic tridiagonal linear systems

Authors: Li, Su-Mei, Fan, Xin, Wang, Yi-Fan

Source: Journal of Mathematical Chemistry. 63:1211-1228

Subject Terms: Linear equations (linear algebraic aspects), Iterative numerical methods for linear systems, cyclic tridiagonal matrices, linear systems, Thomas algorithm, block \textit{LU} factorization, Direct numerical methods for linear systems and matrix inversion, matrix transformation, Factorization of matrices

File Description: application/xml

Extended $$SDD_1^{\dag } $$ matrices and error bounds for linear complementarity problems: Extended \(SDD_1^{\dag}\) matrices and error bounds for linear complementarity problems

Authors: Ran, Wenwen, Wang, Feng

Source: Japan Journal of Industrial and Applied Mathematics. 42:605-630

Subject Terms: \(H\)-matrices, linear complementarity problems, infinity norm bounds, Roundoff error, error bounds, Direct numerical methods for linear systems and matrix inversion, Positive matrices and their generalizations, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

File Description: application/xml

Access URL: https://zbmath.org/8037185
https://doi.org/10.1007/s13160-024-00685-z

A Robust and higher order numerical technique for a time-fractional equation with nonlocal condition: A robust and higher order numerical technique for a time-fractional equation with nonlocal condition

Authors: Taneja, Komal, Deswal, Komal, Kumar, Devendra, Vigo-Aguiar, J.

Source: Journal of Mathematical Chemistry. 63:626-649

Subject Terms: Finite difference methods for boundary value problems involving PDEs, matrix stability, Caputo's derivative, Fractional derivatives and integrals, nonlocal condition, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Direct numerical methods for linear systems and matrix inversion, Fractional partial differential equations, time-fractional reaction-advection-diffusion equation, modified Gauss elimination

File Description: application/xml

Minimization problem solvable by weighted m-weak group inverse: Minimization problem solvable by weighted \(m\)-weak group inverse

Authors: Dijana Mosić, Predrag S. Stanimirović, Lev A. Kazakovtsev

Source: Journal of Applied Mathematics and Computing. 70:6259-6281

Subject Terms: Applications of generalized inverses, weighted core-EP inverse, weighted weak group inverse, Numerical computation of matrix norms, conditioning, scaling, Matrix equations and identities, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Theory of matrix inversion and generalized inverses, Direct numerical methods for linear systems and matrix inversion, weighted \(m\)-weak group inverse

File Description: application/xml

Inertial randomized Kaczmarz algorithms for solving coherent linear systems

Authors: He, Songnian, Wang, Ziting, Dong, Qiao-Li

Source: Numerical Algorithms. 99:133-163

Subject Terms: inertial extrapolation, two-subspace Kaczmarz method, Optimization and Control (math.OC), Randomized algorithms, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Direct numerical methods for linear systems and matrix inversion, randomized Kaczmarz algorithm, inertial randomized Kaczmarz algorithm, Mathematics - Optimization and Control, system of linear equations

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Access URL: http://arxiv.org/abs/2306.08185
https://zbmath.org/8032126
https://doi.org/10.1007/s11075-024-01872-2

Analysis of a generalized MASSOR method for saddle point problems

Authors: Ma, Changfeng, Yu, Xiaojuan

Source: Journal of Computational and Applied Mathematics. 467:116626

Subject Terms: Computational methods for sparse matrices, saddle point problems, GMASSOR method, Direct numerical methods for linear systems and matrix inversion, semi-convergence analysis, convergence analysis

File Description: application/xml

Access URL: https://zbmath.org/8031371
https://doi.org/10.1016/j.cam.2025.116626

High-relative-accuracy computations with Kac-Murdock-Szegö matrices and their generalizations

Authors: Jorge Delgado, J. M. Peña

Source: Zaguán. Repositorio Digital de la Universidad de Zaragoza
Universidad de Zaragoza

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Roundoff error, Kac-Murdock-Szegö matrix, Direct numerical methods for linear systems and matrix inversion, Factorization of matrices, accurate computations

File Description: application/pdf; application/xml

Access URL: http://zaguan.unizar.es/record/153036
https://zbmath.org/8034187
https://doi.org/10.1007/s40314-025-03137-7

Numerical algorithms for the fast and reliable solution of periodic tridiagonal Toeplitz linear systems

Authors: Jia, Ji-Teng, Wang, Yi-Fan

Source: Numerical Algorithms. 98:307-324

Subject Terms: Toeplitz, Cauchy, and related matrices, Toeplitz matrices, linear systems, periodic tridiagonal matrices, Direct numerical methods for linear systems and matrix inversion, Factorization of matrices, matrix decomposition

File Description: application/xml

Access URL: https://zbmath.org/7965179
https://doi.org/10.1007/s11075-024-01795-y

Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm

Authors: Wang, Tao, Li, Ying, Wei, Musheng, Xi, Yimeng, Zhang, Mingcui

Source: Numerical Algorithms. 97:1367-1382

Subject Terms: LU decomposition, real structure-preserving algorithm, Matrices over special rings (quaternions, finite fields, etc.), Direct numerical methods for linear systems and matrix inversion, dual quaternion matrix, Gaussian transformation

File Description: application/xml

Access URL: https://zbmath.org/7932433
https://doi.org/10.1007/s11075-024-01753-8

Communication Avoiding Block Low-Rank Parallel Multifrontal Triangular Solve with Many Right-Hand Sides: Communication avoiding block low-rank parallel multifrontal triangular solve with many right-hand sides

Authors: Amestoy, Patrick, Boiteau, Olivier, Buttari, Alfredo, Gerest, Matthieu, Jézéquel, Fabienne, L’excellent, Jean-Yves, Mary, Theo

Contributors: Mary, Theo, Mumps Technologies Lyon, EDF R&D (EDF R&D), EDF (EDF), Algorithmes Parallèles et Optimisation (IRIT-APO), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Performance et Qualité des Algorithmes Numériques (PEQUAN), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Panthéon-Assas

Source: SIAM Journal on Matrix Analysis and Applications. 45:148-166

Subject Terms: block low-rank matrices, linear systems, Numerical methods for low-rank matrix approximation, matrix compression, [MATH] Mathematics [math], Parallel numerical computation, [INFO] Computer Science [cs], Direct numerical methods for linear systems and matrix inversion, communication avoiding algorithms, Computational methods for sparse matrices, LU factorization, low-rank approximations, numerical linear algebra, data sparse matrices, [INFO]Computer Science [cs], triangular solve, [MATH]Mathematics [math]

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/7791523
https://doi.org/10.1137/23m1568600
https://hal.science/hal-04082415v1/document
https://doi.org/10.1137/23m1568600
https://hal.science/hal-04082415v1

A Simple GPU Implementation of Spectral-Element Methods for Solving 3D Poisson Type Equations on Rectangular Domains and Its Applications: A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on rectangular domains and its applications

Authors: Liu, Xinyu, Shen, Jie, Zhang, Xiangxiong

Source: Communications in Computational Physics. 36:1157-1185

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, Finite difference methods for boundary value problems involving PDEs, FOS: Computer and information sciences, tensor matrix multiplication, rectangular domain, GPU, Parallel numerical computation, spectral element methods, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, direct solver, Computer Science - Distributed, Parallel, and Cluster Computing, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Distributed, Parallel, and Cluster Computing (cs.DC), 3D Poisson equation, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: http://arxiv.org/abs/2310.00226

Splitting ADI Scheme for Fractional Laplacian Wave Equations: Splitting ADI scheme for fractional Laplacian wave equations

Authors: Sun, Tao, Sun, Hai-Wei

Source: Numerical Mathematics: Theory, Methods and Applications. 17:697-726

Subject Terms: Error bounds for initial value and initial-boundary value problems involving PDEs, 65F05, 65M06, 65M12, 65M15, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, alternative direction implicit scheme, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), fractional Laplacian wave equation, Direct numerical methods for linear systems and matrix inversion, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, operator splitting, Gohberg-Semencul formula

File Description: application/xml

Access URL: http://arxiv.org/abs/2312.06206
https://zbmath.org/7966443
https://doi.org/10.4208/nmtma.oa-2023-0149

SlabLU: a two-level sparse direct solver for elliptic PDEs

Authors: Anna Yesypenko, Per-Gunnar Martinsson

Source: Advances in Computational Mathematics. 50

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Numerical Analysis, Random matrices (algebraic aspects), GPU, Numerical methods for low-rank matrix approximation, matrix compression, high-order discretization, Parallel numerical computation, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, multifrontal solver, 01 natural sciences, Factorization of matrices, direct solver, Computational methods for sparse matrices, Numerical algorithms for specific classes of architectures, Boundary value problems for second-order elliptic equations, sparse direct solver, FOS: Mathematics, Spectral, collocation and related methods for boundary value problems involving PDEs, randomized linear algebra, Helmholtz equation, 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/2211.07572

Second‐order accurate hierarchical approximate factorizations for solving sparse linear systems: Second-order accurate hierarchical approximate factorizations for solving sparse linear systems

Authors: Bazyli Klockiewicz, Léopold Cambier, Ryan Humble, Hamdi Tchelepi, Eric Darve

Source: International Journal for Numerical Methods in Engineering. 123:5473-5499

Subject Terms: Computational methods for sparse matrices, preconditioner, second-order, Preconditioners for iterative methods, nested dissection, 0101 mathematics, Direct numerical methods for linear systems and matrix inversion, linear solver, low-rank, 01 natural sciences

File Description: application/xml

Inversion of block Toeplitz and Hankel matrices

Authors: Katai, I., Rahmy, E.

Source: Publicationes Mathematicae Debrecen. 26:139-147

Subject Terms: block Toeplitz and Hankel matrices, band matrices, inverse of a Hermitian Toeplitz matrix, recursion formulas, Hermitian, skew-Hermitian, and related matrices, Theory of matrix inversion and generalized inverses, band matrix, 0101 mathematics, Direct numerical methods for linear systems and matrix inversion, Trench's algorithm, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3692517

High-order weighted compact nonlinear scheme for solving degenerate parabolic equations

Authors: Yinggang Hu, Yanqun Jiang, Xiaoqian Huang, Wei Zhang

Source: Computational and Applied Mathematics. 43

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, discontinuity-capturing ability, Numerical interpolation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, weighted compact nonlinear scheme, high-order accurate, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Direct numerical methods for linear systems and matrix inversion, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Degenerate parabolic equations, nonlinear degenerate parabolic equations, non-oscillatory property

File Description: application/xml

Access URL: https://zbmath.org/7803448
https://doi.org/10.1007/s40314-023-02551-z

Determinants and inverses of weighted Loeplitz and weighted Foeplitz matrices and their applications in data encryption

Authors: Meng, Qingyan, Zheng, Yanpeng, Jiang, Zhaolin

Source: Journal of Applied Mathematics and Computing. 68:3999-4015

Subject Terms: Toeplitz, Cauchy, and related matrices, inverse, Determinants, permanents, traces, other special matrix functions, weighted Foeplitz matrix, Fibonacci numbers, Matrices, determinants in number theory, Direct numerical methods for linear systems and matrix inversion, determinant, Lucas numbers, 01 natural sciences, Numerical computation of determinants, weighted Loeplitz matrix, Theory of matrix inversion and generalized inverses, 0101 mathematics, data and image encryption

File Description: application/xml

Access URL: https://zbmath.org/7632335
https://doi.org/10.1007/s12190-022-01700-7

Re-analysis method for inversion of block matrix based on change threshold

Authors: Huping Mao, Biliang Cheng, Peng Zhang, Feng Jia, Quan Sun

Source: Applied Mathematical Modelling. 94:780-790

Subject Terms: Finite element methods applied to problems in solid mechanics, 0203 mechanical engineering, reanalysis, change threshold, block inversion, 02 engineering and technology, 0101 mathematics, Direct numerical methods for linear systems and matrix inversion, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7424292
https://doi.org/10.1016/j.apm.2021.01.045
https://www.sciencedirect.com/science/article/pii/S0307904X21000652

Randomized compression of rank-structured matrices accelerated with graph coloring

Authors: James Levitt, Per-Gunnar Martinsson

Source: Journal of Computational and Applied Mathematics. 451:116044

Subject Terms: Random matrices (algebraic aspects), HODLR matrix, Numerical linear algebra, Randomized algorithms, hierarchically block separable matrix, Boundary element methods for boundary value problems involving PDEs, Numerical Analysis (math.NA), Numerical solution of discretized equations for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, 01 natural sciences, Factorization of matrices, Computational methods for sparse matrices, hierarchically semiseparable matrix, rank-structured matrices, randomized approximation of matrices, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, 65N22, 65N38, 15A23, 15A52, fast direct solver

File Description: application/xml

Access URL: http://arxiv.org/abs/2205.03406