Results 31 to 40 of about 4,826 (176)
AlgorithmsGMRES is one of the most powerful and popular methods to solve linear systems in the Krylov subspace; we examine it from two viewpoints: to maximize the decreasing length of the residual vector, and to maintain the orthogonality of the consecutive ...
Chein-Shan Liu +2 more
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Frontiers in Physics, 2022 The aim of this paper is to propose some efficient and accurate numerical methods to compute the steady-state of variable coefficients space fractional Cahn-Allen equations.
Saleh Mousa Alzahrani +1 more
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Stabilizing randomized GMRES through flexible GMRES
CoRRWe explore the use of flexible GMRES as an outer wrapper for sketched GMRES. Building on a new bound for the residual of FGMRES in terms of the residual of the preconditioner, we derive a practical randomized solver that requires very little parameter tuning, while still being efficient and robust in the sense of generating non-increasing residual ...
Stefan Güttel, John W. Pearson
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ILU preconditioning based on the FAPINV algorithm [PDF]
Opuscula Mathematica, 2015 A technique for computing an ILU preconditioner based on the factored approximate inverse (FAPINV) algorithm is presented. We show that this algorithm is well-defined for H-matrices.
Davod Khojasteh Salkuyeh +2 more
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SICE Journal of Control, Measurement, and System Integration, 2019 We consider solving a large-scale Lyapunov equation for a multi-agent system. As is well known, the Lyapunov equation can be solved by equivalently rewriting it as a system of linear equations.
Asuka Ohashi, Kiyotsugu Takaba
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Computable Convergence Bounds for GMRES [PDF]
SIAM Journal on Matrix Analysis and Applications, 2000 The purpose of this paper is to derive new computable convergence bounds for GMRES. The new bounds depend on the initial guess and are thus conceptually different from standard "worst-case" bounds. Most importantly, approximations to the new bounds can be computed from information generated during the run of a certain GMRES implementation.
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On the regularizing properties of the GMRES method [PDF]
Numerische Mathematik, 2002 The generalized minimal residual (GMRES) method equipped with a stopping criterion based on the discrepancy principle is used to solve nonsymmetric nonsingular ill-posed problems with a right-hand side contaminated with errors. When the inverse operator \(A^{-1}\) of the linear system \(Ax=b\) is not bounded and the exact right-hand side \(b\) is not ...
Daniela Calvetti +2 more
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Um Esquema GMRES Precondicionado para Simulação de Reservatórios
Trends in Computational and Applied Mathematics, 2002 Descrevemos um método GMRES precondicionado para a resolução de sistemas lineares que aparecem em Simulação de Reservatórios de Petróleo. Três esquemas de precondicionamento são propostos.
L.M. CARVALHO +3 more
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Trends in Computational and Applied Mathematics, 2022 Neste artigo o método multigrid algébrico baseado em agregação suavizada, o método clássico de Ruge-Stüben e o método GMRES pré-condicionado por multigrid algébrico foram utilizados para a solução da equação do fluxo livre estacionário em domínio ...
J. P. M. dos Santos +3 more
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Preconditioning GMRES for discontinuous Galerkin approximations
Computer Assisted Methods in Engineering and Science, 2023 The paper presents an implementation and the performance of several preconditioners for the discontinuous Galerkin approximation of diffusion dominated and pure diffusion problems.
Krzysztof Banaś, Mary F. Wheeler
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