Search Results - "computational methods for sparse matrices"

A Low-Memory Lanczos Method with Rational Krylov Compression for Matrix Functions: A low-memory Lanczos method with rational Krylov compression for matrix functions

Authors: Angelo A. Casulli Igor Simunec

Source: SIAM Journal on Scientific Computing. 47:A1358-A1382

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, Computational methods for sparse matrices, matrix function, 65F60, 65F50, Mathematics - Numerical Analysis, rational Krylov, low memory

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Access URL: http://arxiv.org/abs/2403.04390

Construction of hierarchically semiseparable matrix representation using adaptive Johnson–Lindenstrauss sketching: Construction of hierarchically semiseparable matrix representation using adaptive Johnson-Lindenstrauss sketching

Authors: Yaniv, Yotam Ghysels, Pieter Malik, Osman Asif et al.

Source: Communications in Applied Mathematics and Computational Science. 20:67-117

Subject Terms: randomized sampling, Numerical linear algebra, Randomized algorithms, 0102 computer and information sciences, Numerical Analysis (math.NA), HSS matrix, 01 natural sciences, Special classes of linear operators, Johnson-Lindenstrauss sketching, adaptivity, Computational methods for sparse matrices, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics

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Access URL: http://arxiv.org/abs/2302.01977
https://zbmath.org/8034689
https://doi.org/10.2140/camcos.2025.20.67

Fast breakdown-free algorithm for computing the determinants of a generalized comrade matrix

Authors: Fan, Xin Jia, Ji-Teng

Source: Journal of Mathematical Chemistry. 63:1189-1210

Subject Terms: Computational methods for sparse matrices, tridiagonal matrices, determinants, Determinants, permanents, traces, other special matrix functions, generalized comrade matrices, incomplete block-diagonalizations, breakdown-free algorithm, Numerical computation of determinants, comrade matrices

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Access URL: https://zbmath.org/8035157
https://doi.org/10.1007/s10910-025-01714-z

Solution Decomposition for the Nonlinear Poisson–Boltzmann Equation Using the Range-Separated Tensor Format: Solution decomposition for the nonlinear Poisson-Boltzmann equation using the range-separated tensor format

Authors: Cleophas Kweyu Venera Khoromskaia Boris N. Khoromskij et al.

Source: SIAM Journal on Scientific Computing. 47:B87-B107

Subject Terms: Iterative numerical methods for linear systems, Numerical linear algebra, G.1.8, G.1.3, 65F30, 65F50, 65N35, 65F10, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Electro- and magnetostatics, 01 natural sciences, Computational methods for sparse matrices, Multilinear algebra, tensor calculus, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Poisson-Boltzmann equation, low-rank tensor decompositions, range-separated tensor formats

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Access URL: http://arxiv.org/abs/2109.14073
http://hdl.handle.net/21.11116/0000-0009-4AD3-6
http://hdl.handle.net/21.11116/0000-0009-4AD5-4

A Multigrid Reduction Framework for Domains with Symmetries: A multigrid reduction framework for domains with symmetries

Authors: Alsalti Baldellou, Àdel Janna, Carlo Álvarez Farré, Xavier et al.

Source: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Subject Terms: Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids, FOS: Computer and information sciences, Àrees temàtiques de la UPC::Física::Termodinàmica, Multigrid methods, domain decomposition for boundary value problems involving PDEs, Spatial symmetries, spatial symmetries, Navier-Stokes equations for incompressible viscous fluids, Parallel numerical computation, Numerical Analysis (math.NA), Computational methods for sparse matrices, Poisson's equation, Computer Science - Distributed, Parallel, and Cluster Computing, AMG, multigrid reduction, FOS: Mathematics, Multigrid reduction, Preconditioners for iterative methods, SpMM, Mathematics - Numerical Analysis, Distributed, Parallel, and Cluster Computing (cs.DC), 65F08, 65F50, 65N55, 65Y05

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Access URL: http://arxiv.org/abs/2407.05930
https://hdl.handle.net/11577/3552922
https://doi.org/10.1137/24M1638513

Symbolic algorithm for solving SLAEs with multi-diagonal coefficient matrices

Authors: Veneva Milena

Source: Discrete and Continuous Models and Applied Computational Science, Vol 33, Iss 1, Pp 46-56 (2025)

Subject Terms: numerical analysis, computational methods for sparse matrices, numerical mathematical programming methods, complexity of numerical algorithms, Electronic computers. Computer science, QA75.5-76.95

File Description: electronic resource

Relation: https://journals.rudn.ru/miph/article/viewFile/44732/24876; https://doaj.org/toc/2658-4670; https://doaj.org/toc/2658-7149

Access URL: https://doaj.org/article/f9e3c5410dc44f88b856ee50ce4a6554

A modified improved alternating positive semi-definite splitting preconditioner for double saddle point problems

Authors: Jun Li Shu-Xin Miao Xiangtuan Xiong

Source: Journal of Applied Mathematics and Computing. 70:5081-5101

Subject Terms: Iterative numerical methods for linear systems, Computational methods for sparse matrices, convergence, iteration method, GMRES method, Preconditioners for iterative methods, double saddle point problems, mixed Stokes/Darcy model, liquid crystal director model

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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

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

A Hybrid Collocation Method for Long‐Time Simulation of Heat Conduction in Anisotropic Functionally Graded Materials: A hybrid collocation method for long-time simulation of heat conduction in anisotropic functionally graded materials

Authors: Lin Qiu Fajie Wang Wenzhen Qu et al.

Source: International Journal for Numerical Methods in Engineering. 126

Subject Terms: Iterative numerical methods for linear systems, anisotropic heat conduction, Numerical radial basis function approximation, Numerical computation of solutions to systems of equations, Diffusive and convective heat and mass transfer, heat flow, radial basis function collocation method, Finite difference methods applied to problems in solid mechanics, Computational methods for sparse matrices, Thermal effects in solid mechanics, Krylov deferred correction technique, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, long-time simulation, PDEs in connection with mechanics of deformable solids, functionally graded materials, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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Access URL: https://zbmath.org/7991422
https://doi.org/10.1002/nme.70002

A Grid-Overlay Finite Difference Method for Inhomogeneous Dirichlet Problems of the Fractional Laplacian on Arbitrary Bounded Domains: A grid-overlay finite difference method for inhomogeneous Dirichlet problems of the fractional Laplacian on arbitrary bounded domains

Authors: Weizhang Huang Jinye Shen

Source: Journal of Scientific Computing. 102

Subject Terms: Finite difference methods for boundary value problems involving PDEs, overlay grid, finite difference, mesh adaptation, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Fractional partial differential equations, Computational methods for sparse matrices, Error bounds for initial value and initial-boundary value problems involving PDEs, Fractional derivatives and integrals, inhomogeneous fractional Laplacian, Preconditioners for iterative methods, arbitrary domain, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Numerical methods for discrete and fast Fourier transforms

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Access URL: https://zbmath.org/7975323
https://doi.org/10.1007/s10915-024-02782-0

Hierarchical Interpolative Factorization for Self Green’s Function in 3D Modified Poisson-Boltzmann Equations: Hierarchical interpolative factorization for self Green's function in 3D modified Poisson-Boltzmann equations

Authors: Yihui Tu Zhenli Xu Haizhao Yang

Source: Communications on Applied Mathematics and Computation. 7:536-561

Subject Terms: Computational methods for sparse matrices, self Green's function, modified Poisson-Boltzmann (MPB) equations, hierarchical interpolative factorization, FOS: Physical sciences, Numerical solution of discretized equations for boundary value problems involving PDEs, Computational Physics (physics.comp-ph), linear scaling, Physics - Computational Physics, Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics, selected inversion

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Access URL: http://arxiv.org/abs/2307.01060
https://zbmath.org/8034289
https://doi.org/10.1007/s42967-023-00352-z

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 et al.

Contributors: Amestoy, Patrick Boiteau, Olivier Buttari, Alfredo et al.

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]

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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

An improved model order reduction method for dynamic analysis of large-scale structures with local nonlinearities

Authors: Li, Wenxiong Chen, Suiyin

Source: Applied Mathematical Modelling. 120:786-811

Subject Terms: Computational methods for sparse matrices, model order reduction, iteration solution algorithm, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, dynamic analysis, local nonlinearity, time integration method, Orthogonalization in numerical linear algebra

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An Incomplete Cholesky Preconditioner Based on Orthogonal Approximations: An incomplete Cholesky preconditioner based on orthogonal approximations

Authors: Napov, Artem

Source: SIAM Journal on Scientific Computing. 45:A729-A752

Subject Terms: orthogonal approximations, Computational methods for sparse matrices, preconditioner, Numerical computation of matrix norms, conditioning, scaling, low-rank approximations, breakdown-free incomplete Cholesky, Preconditioners for iterative methods, 0101 mathematics, conditioning analysis, 01 natural sciences, Analyse numérique, Programmation du calcul numérique, sparse incomplete Cholesky

File Description: application/xml; 2 full-text file(s): application/pdf; application/pdf

Access URL: https://zbmath.org/7682229
https://doi.org/10.1137/21m1468334

Recursive Algorithms to Update a Numerical Basis Matrix of the Null Space of the Block Row, (Banded) Block Toeplitz, and Block Macaulay Matrix

Authors: Vermeersch, Christof De Moor, Bart

Source: SIAM Journal on Scientific Computing

Subject Terms: Science & Technology, 0103 Numerical and Computational Mathematics, Mathematics, Applied, STADIUS-21-111, orthogonalization, Numerical & Computational Mathematics, computational methods for sparse matrices, REALIZATION, SYSTEMS, 0102 Applied Mathematics, Physical Sciences, 4903 Numerical and computational mathematics, 4901 Applied mathematics, block Toeplitz and block Macaulay matrices, Mathematics, 0802 Computation Theory and Mathematics

Access URL: https://lirias.kuleuven.be/handle/20.500.12942/719879
https://doi.org/10.1137/22m1495858

Computational methods for sparse matrices

Authors: C.M.M. Nex

Source: Computer Physics Communications. 20:7-10

Subject Terms: 0101 mathematics, 01 natural sciences

Access URL: http://ui.adsabs.harvard.edu/abs/1980CoPhC..20....7N/abstract
https://www.sciencedirect.com/science/article/pii/0010465580901009

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

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

On Cvetković-Kostić-Varga type matrices

Authors: Gao, Lei Li, Chaoqian

Source: ETNA - Electronic Transactions on Numerical Analysis. 58:244-270

Subject Terms: \(H\)-matrices, Computational methods for sparse matrices, \(S\)-sparse Ostrowski-Brauer type-I matrices, Special matrices, CKV-type matrices, \(S\)-sparse Ostrowski-Brauer type-II matrices

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Access URL: https://zbmath.org/7693751
https://doi.org/10.1553/etna_vol58s244

Numerical Solutions of the Electromagnetic Scattering by Overfilled Cavities with Inhomogeneous Anisotropic Media: Numerical solutions of the electromagnetic scattering by overfilled cavities with inhomogeneous anisotropic media

Authors: Zhao, Meiling He, Jiahui Wang, Liqun

Source: Communications in Computational Physics. 34:530-562

Subject Terms: Variational methods applied to problems in optics and electromagnetic theory, Computational methods for sparse matrices, Iterative numerical methods for linear systems, Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory, Maxwell equations, electromagnetic scattering, Petrov-Galerkin finite element interface method, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, inhomogeneous anisotropic media, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, overfilled cavity, Diffraction, scattering, non-body-fitted grids

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Access URL: https://zbmath.org/7784443
https://doi.org/10.4208/cicp.oa-2022-0104

Meshfree generalized multiscale exponential integration method for parabolic problems

Authors: Djulustan Nikiforov Leonardo A. Poveda Dmitry Ammosov et al.

Source: Journal of Computational and Applied Mathematics. 459:116367

Subject Terms: time integration, Flows in porous media, filtration, seepage, Numerical computation of matrix norms, conditioning, scaling, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDEs in connection with fluid mechanics, 01 natural sciences, Finite difference methods applied to problems in fluid mechanics, meshfree generalized multiscale finite element method, Computational methods for sparse matrices, exponential integrator, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Semilinear parabolic equations, parabolic problems, Finite element methods applied to problems in fluid mechanics

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Access URL: http://arxiv.org/abs/2408.05005