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

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

Hierarchical Orthogonal Factorization: Sparse Square Matrices: Hierarchical orthogonal factorization: sparse square matrices

Authors: Abeynaya Gnanasekaran Eric Darve

Source: SIAM Journal on Matrix Analysis and Applications. 43:94-123

Subject Terms: Householder reflections, 65F08 (Primary), 65F25, 65F50, 65Y20, 65F05 (Secondary), Numerical Analysis (math.NA), G.1.3, low-rank, 01 natural sciences, Orthogonalization in numerical linear algebra, Computational methods for sparse matrices, Complexity and performance of numerical algorithms, hierarchical factorization, sparse linear solver, FOS: Mathematics, Preconditioners for iterative methods, nested dissection, Mathematics - Numerical Analysis, 0101 mathematics

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Access URL: http://arxiv.org/pdf/2010.06807
http://arxiv.org/abs/2010.06807
https://zbmath.org/7471934
https://doi.org/10.1137/20m1373475

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

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 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

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

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

File Description: application/pdf; application/xml

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

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

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 et al.

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

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Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones

Authors: Andersen, Martin S. Dahl, Joachim Vandenberghe, Lieven

Source: Mathematical Programming Computation: A Publication of the Mathematical Optimization Society. 2(3)

Subject Terms: Mathematics, Operations Research/Decision Theory, Optimization, 90-08 Mathematical Programming - computational methods, 90C06 Mathematical Programming - large-scale, 90C22 Mathematical Programming - semidefinite programing, 90C25 Mathematical Programming - convex programming, 90C51 Mathematical Programming - interior-point methods

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Access URL: https://escholarship.org/uc/item/2175g56s
https://escholarship.org/content/qt2175g56s/qt2175g56s.pdf

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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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

A New Sparse-Matrix Storage Method for Adaptively Solving Large Systems of Reaction-Diffusion-Transport Equations: A new sparse-matrix storage method for adaptively solving large systems of reaction-diffusion-transport equations

Authors: Nicolas Neuß

Source: Scientific Computing in Chemical Engineering II ISBN: 9783642642951

Subject Terms: box method, Iterative numerical methods for linear systems, sparse-matrix storage method, reaction-diffusion-transport equations, compact row-ordered storage, matrix-vector multiplication, compact storage, chemical reactions, finite volume method, 01 natural sciences, stabilization, Computational methods for sparse matrices, Reaction-diffusion equations, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, iterative methods, matrix graph, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Chemically reacting flows, multigrid

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Access URL: https://link.springer.com/content/pdf/10.1007/s006070200001.pdf
https://rd.springer.com/chapter/10.1007/978-3-642-60185-9_19
https://link.springer.com/article/10.1007/s006070200001
https://dblp.uni-trier.de/db/journals/computing/computing68.html#Neuss02

A Two-Dimensional Data Distribution Method for Parallel Sparse Matrix-Vector Multiplication: A two-dimensional data distribution method for parallel sparse matrix-vector multiplication

Authors: Vastenhouw, B. Bisseling, R.H. Analyse et al.

Contributors: Vastenhouw, B. Bisseling, R.H. Analyse et al.

Source: SIAM Review. 47:67-95

Subject Terms: sparse matrix, Iterative numerical methods for linear systems, numerical examples, Graphs and linear algebra (matrices, eigenvalues, etc.), parallel computing, Wiskunde en computerwetenschappen, Other matrix algorithms, matrix-vector multiplication, Parallel numerical computation, 01 natural sciences, Computational methods for sparse matrices, recursive bipartitioning, Landbouwwetenschappen, Wiskunde: algemeen, Wiskunde en Informatica (WIIN), matrix partitioning, 0101 mathematics, Mathematics

File Description: application/xml; image/pdf

Access URL: http://dspace.library.uu.nl/bitstream/1874/203492/1/4-40901.pdf
https://zbmath.org/2205840
https://doi.org/10.1137/s0036144502409019
https://research-portal.uu.nl/en/publications/e83d2b9f-8725-4ea5-b164-a2a4e0d7f52f
https://doi.org/10.1137/S0036144502409019
https://dspace.library.uu.nl/handle/1874/203492

Computational experience with sequential and parallel, preconditioned Jacobi–Davidson for large, sparse symmetric matrices: Computational experience with sequential and parallel, preconditioned Jacobi--Davidson for large, sparse symmetric matrices

Authors: BERGAMASCHI, LUCA PINI, GIORGIO SARTORETTO, FLAVIO

Source: Journal of Computational Physics. 188:318-331

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, large, sparse matrices, approximate inverse preconditioners, convergence, paralell algorithms, Numerical computation of matrix norms, conditioning, scaling, eigenvalues, parallel algorithms, sparse approximate inverses, Jcobi-Davidson method, Parallel numerical computation, 01 natural sciences, Computational methods for sparse matrices, preconditioning, Jacobi-Davidson method, 0101 mathematics, performance

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Access URL: http://www.dmsa.unipd.it/~berga/Research/Eigen/jcp.pdf
https://zbmath.org/1957083
https://doi.org/10.1016/s0021-9991(03)00190-6
https://www.sciencedirect.com/science/article/pii/S0021999103001906
https://www.research.unipd.it/handle/11577/2467673
http://www.sciencedirect.com/science/article/pii/S0021999103001906
https://iris.unive.it/handle/10278/14530
https://ui.adsabs.harvard.edu/abs/2003JCoPh.188..318B/abstract
http://www.dmsa.unipd.it/~berga/Research/Eigen/jcp.pdf
https://hdl.handle.net/10278/14530
http://www.sciencedirect.com/science/article/pii/S0021999103001906
https://doi.org/10.1016/S0021-9991(03)00190-6
https://hdl.handle.net/11577/2467673

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