Search Results - "Iterative numerical methods for linear systems"

On the greedy coordinate descent methods for solving large linear least-squares problems

Authors: Dong, Qin Zhang, Nai-Min

Source: Japan Journal of Industrial and Applied Mathematics. 42:813-830

Subject Terms: Iterative numerical methods for linear systems, maximization, convergence, greedy coordinate descent, Numerical computation of matrix norms, conditioning, scaling, randomization, least-squares problem

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Frequency Range of a Non-Lipschitz Parametric Optimization of a Noise Absorption: Frequency range of a non-Lipschitz parametric optimization of a noise absorption

Authors: Frédéric Magoulès Mathieu Menoux Anna Rozanova-Pierrat

Source: SIAM Journal on Control and Optimization. 63:1267-1285

Subject Terms: Linear equations (linear algebraic aspects), Iterative numerical methods for linear systems, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Boundary value problems for second-order elliptic equations, sound absorption, wave propagation, \(d\)-upper regular measure, parametric shape optimization, Helmholtz equation, Numerical solution of discretized equations for boundary value problems involving PDEs, Robin boundary condition, First-order hyperbolic systems

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A block coordinate descent linear least squares solver by quantile statistics

Authors: Zhang, Ke Deng, Jin-Yu Jiang, Xiang-Long

Source: Japan Journal of Industrial and Applied Mathematics. 42:787-811

Subject Terms: Iterative numerical methods for linear systems, quantile, Numerical solutions to overdetermined systems, pseudoinverses, Numerical computation of solutions to systems of equations, least squares problem, randomized coordinate descent, Kaczmarz algorithm

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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

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Convergence of the modified Newton-type iteration method for the generalized absolute value equation

Authors: Fang, Ximing Huang, Minhai

Source: Arabian Journal of Mathematics. 14:29-37

Subject Terms: Iterative numerical methods for linear systems, Mathematical programming, Methods of quasi-Newton type

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DeepONet Based Preconditioning Strategies for Solving Parametric Linear Systems of Equations: DeepONet based preconditioning strategies for solving parametric linear systems of equations

Authors: Alena Kopaničáková George Em Karniadakis

Source: SIAM Journal on Scientific Computing. 47:C151-C181

Subject Terms: Large-scale problems in mathematical programming, Iterative numerical methods for linear systems, operator learning, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, preconditioning, Learning and adaptive systems in artificial intelligence, FOS: Mathematics, Krylov methods, Preconditioners for iterative methods, spectral bias, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), hybridization

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Access URL: http://arxiv.org/abs/2401.02016

A two-level overlapping Schwarz preconditioner for discontinuous Galerkin methods

Authors: Calvo, Juan G. Solano, Moisés

Source: Revista de Matemática: Teoría y Aplicaciones. 32:15-33

Subject Terms: Iterative numerical methods for linear systems, domain decomposition, discontinuous Galerkin methods, nodal elliptic problems, Multigrid methods, domain decomposition for boundary value problems involving PDEs, Preconditioners for iterative methods, irregular subdomain boundaries, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, overlapping Schwarz algorithms

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A new two-parameter iteration method for solving absolute value equations

Authors: Xiao-Yong Xiao Miao Zhang

Source: Japan Journal of Industrial and Applied Mathematics. 42:631-652

Subject Terms: Iterative numerical methods for linear systems, Numerical optimization and variational techniques, Numerical computation of solutions to systems of equations, iteration method, absolute value equations, linear complementarity problem, convergence analysis

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Access URL: https://zbmath.org/8037186
https://doi.org/10.1007/s13160-024-00687-x

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

THE EFFECTIVE AND MODIFIED JACOBI GRADIENT BASED ITERATIVE ALGORITHMS FOR THE DISCRETE-TIME PERIODIC SYLVESTER MATRIX EQUATIONS: The effective and modified Jacobi gradient based iterative algorithms for the discrete-time periodic Sylvester matrix equations

Authors: Wu, Xiaowen Huang, Zhengge

Source: Journal of Applied Analysis & Computation. 15:2044-2088

Subject Terms: Iterative numerical methods for linear systems, convergence properties, MJGI algorithm, Numerical computation of solutions to systems of equations, DTPS matrix equations, GDTPS matrix equations, EJGI algorithm

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Access URL: https://zbmath.org/8010857
https://doi.org/10.11948/20240393

A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids

Authors: Meijie Kong Hongfei Fu

Source: Fractional Calculus and Applied Analysis. 27:3446-3476

Subject Terms: Iterative numerical methods for linear systems, fractional block-centered finite difference method, nonuniform grids, Mathematics - Analysis of PDEs, space-fractional diffusion equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), fast matrix-vector multiplication, Fractional partial differential equations, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2312.10577
https://zbmath.org/7996702
https://doi.org/10.1007/s13540-024-00346-5

A recent fixed point method based on two inertial terms

Authors: Inkrong, Papatsara Paimsang, Papinwich Cholamjiak, Prasit

Source: The Journal of Analysis. 33:521-535

Subject Terms: Iterative numerical methods for linear systems, inertial extrapolation, Fixed-point theorems, fixed point iteration, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc, weak convergence, nonexpansive mapping

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Access URL: https://zbmath.org/8035908
https://doi.org/10.1007/s41478-024-00845-x

A Scalable Two-Level Domain Decomposition Eigensolver for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains: A scalable two-level domain decomposition eigensolver for periodic Schrödinger eigenstates in anisotropically expanding domains

Authors: Lambert Theisen Benjamin Stamm

Source: SIAM Journal on Scientific Computing. 46:A3067-A3093

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, FOS: Computer and information sciences, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Iterative numerical methods for linear systems, Multigrid methods, domain decomposition for boundary value problems involving PDEs, finite element method, Schrödinger equation, 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, coarse spaces, Computational Engineering, Finance, and Science (cs.CE), domain decomposition, preconditioning, FOS: Mathematics, iterative methods, 65N25, 65F15, 65N30, 65F10, 65N22, 65N55, 65F08, Preconditioners for iterative methods, Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science

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Access URL: http://arxiv.org/abs/2311.08757

Improvement of Convergence of One- and Two-Step MSM Iteration Methods for Nondifferentiable Nonlinear Complementarity Problems: Improvement of convergence of one- and two-step MSM iteration methods for nondifferentiable nonlinear complementarity problems

Authors: Gui-Lin Yan Yu-Jiang Wu Bo Deng

Source: Communications on Applied Mathematics and Computation. 7:733-758

Subject Terms: nonlinear complementarity problem (NCP), Iterative numerical methods for linear systems, convergence, Numerical mathematical programming methods, modulus-based, multisplitting, \(H_+\)-matrix, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), \(H\)-splitting

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Access URL: https://zbmath.org/8034297
https://doi.org/10.1007/s42967-024-00378-x

Analysis and numerical simulation of a generalized compressible Cahn–Hilliard–Navier–Stokes model with friction effects: Analysis and numerical simulation of a generalized compressible Cahn-Hilliard-Navier-Stokes model with friction effects

Authors: Elbar, Charles Poulain, Alexandre Sciences, EDP

Contributors: Elbar, Charles Poulain, Alexandre Sciences, EDP

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 58:1989-2034

Subject Terms: Cell biology, Iterative numerical methods for linear systems, scalar auxiliary variable method, 35B40, 35B45, 35G20, 35Q35, 35Q92, 65M08, PDEs in connection with biology, chemistry and other natural sciences, Nonlinear higher-order PDEs, [MATH] Mathematics [math], PDEs in connection with fluid mechanics, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, Physiological flows, 01 natural sciences, Cahn-Hilliard equation, Navier-Stokes equation, numerical simulations, Fixed-point theorems, Mathematics - Analysis of PDEs, FOS: Mathematics, Cahn–Hilliard equation, Mathematics - Numerical Analysis, 0101 mathematics, Weak solutions to PDEs, Physiological flow, Navier–Stokes equation, Asymptotic behavior of solutions to PDEs, mathematical modeling, Existence problems for PDEs: global existence, local existence, non-existence, Numerical Analysis (math.NA), A priori estimates in context of PDEs, asymptotic analysis, Friction in solid mechanics, Finite element, Rayleigh-Ritz and Galerkin 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, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2305.05623
https://hal.science/hal-04747238v1
https://hal.science/hal-04747238v1/document
https://doi.org/10.1051/m2an/2024063

An Uzawa-DOS method for solving saddle-point problems

Authors: Ebadi, Ghodrat Mehrabi, Khosro Stanimirović, Predrag S.

Source: Numerical Algorithms. 99:165-182

Subject Terms: Iterative numerical methods for linear systems, convergence, iteration method, linear system, Uzawa method

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Access URL: https://zbmath.org/8032127
https://doi.org/10.1007/s11075-024-01873-1

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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A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model: A two-level Crank-Nicolson difference scheme and its Richardson extrapolation methods for a magneto-thermo-elasticity model

Authors: Deng, Dingwen Zhang, Ruyu

Source: Advances in Applied Mathematics and Mechanics. 16:608-635

Subject Terms: Finite difference methods for boundary value problems involving PDEs, energy conservation, Iterative numerical methods for linear systems, Extrapolation to the limit, deferred corrections, convergence, Richardson extrapolation methods, priori estimation, Symbolic computation and algebraic computation, Finite difference methods applied to problems in solid mechanics, Thermal effects in solid mechanics, Electromagnetic effects in solid mechanics, Classical linear elasticity, 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, finite difference method, solvability

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A Low-Rank Global Krylov Squared Smith Method for Solving Large-Scale Stein Matrix Equation: A low-rank global Krylov squared Smith method for solving large-scale Stein matrix equation

Authors: Nie, Song Dai, Hua

Source: Communications on Applied Mathematics and Computation. 7:562-588

Subject Terms: Iterative numerical methods for linear systems, Numerical methods for matrix equations, Stein matrix equation, squared Smith method, Lyapunov matrix equation, restart technique, global Krylov subspace

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A dimension expanded Newton-type method for absolute value equations

Authors: Wei-Hua Luo Jun Guo Liang Yin

Source: Journal of Applied Mathematics and Computing. 70:3219-3233

Subject Terms: Iterative numerical methods for linear systems, Newton method, Numerical computation of roots of polynomial equations, quadratic polynomial equations, absolute value equations, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

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Access URL: https://zbmath.org/7895371
https://doi.org/10.1007/s12190-024-02093-5