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Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring. [PDF]
PLoS ONEWe propose an efficient preconditioning strategy to accelerate the convergence of Krylov subspace methods, specifically for solving complex nonlinear systems with a block five-by-five structure, commonly found in cell-centered finite difference ...
Rizwan Khalid +4 more
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Adaptive GMRES(m) for the Electromagnetic Scattering Problem
Trends in Computational and Applied Mathematics, 2020 In this article, an adaptive version of the restarted GMRES (GMRES(m)) is introduced for the resolution of the finite difference approximation of the Helmholtz equation. It has been observed that the choice of the restart parameter m strongly affects the
Gustavo Espínola +2 more
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Multipreconditioned GMRES for simulating stochastic automata networks
Open Mathematics, 2018 Stochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their ...
Wen Chun +5 more
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Electrocardiographic Imaging: A Comparison of Iterative Solvers [PDF]
Frontiers in Physiology, 2021 Cardiac disease is a leading cause of morbidity and mortality in developed countries. Currently, non-invasive techniques that can identify patients at risk and provide accurate diagnosis and ablation guidance therapy are under development.
Marta Borràs, Judit Chamorro-Servent
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GMRES and Integral Operators [PDF]
SIAM Journal on Scientific Computing, 1996 The purpose of this paper is to show how the generalized minimal residual (GMRES) method can be modified to incorporate Nyström interpolation at a small cost in both computational effort and algorithmic complexity. The result is an algorithm that has the convergence property of Broyden's method.
C. T. Kelley, Z. Q. Xue
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GMRES convergence bounds for eigenvalue problems [PDF]
Computational Methods in Applied Mathematics, 2016 Abstract The convergence of GMRES for solving linear systems can be influenced heavily by the structure of the right-hand side. Within the solution of eigenvalue problems via inverse iteration or subspace iteration, the right-hand side is generally related to an approximate invariant subspace of the linear system.
Melina A. Freitag +2 more
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Augmented GMRES‐type methods [PDF]
Numerical Linear Algebra with Applications, 2007 AbstractGMRES is a popular iterative method for the solution of large linear systems of equations with a square non‐symmetric matrix. The method generates a Krylov subspace in which an approximate solution is determined. We present modifications of the GMRES and the closely related RRGMRES methods that allow augmentation of the Krylov subspaces ...
James Baglama, Lothar Reichel
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An efficient iterative method for solving large linear systems [PDF]
Journal of Hyperstructures, 2020 This paper presents a new powerful iterative method for solving large and sparse linear systems. Using the idea of theJaya method to the restarted generalized minimum residual (GMRES) method, we propose the Jaya-GMRES method.The JayaGMRES is an efficient
Ali Jamalian, Hossein Aminikhah
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Fluids, 2021 Newton’s method has been widely used in simulation multiphase, multicomponent flow in porous media. In addition, to solve systems of linear equations in such problems, the generalized minimal residual method (GMRES) is often used. This paper analyzed the
Timur Imankulov +4 more
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Weighted Inner Products for GMRES and GMRES-DR [PDF]
SIAM Journal on Scientific Computing, 2017 Revision containing edits to the text, corrections, and removal of the section on Arnoldi in weighted inner products (to reduce the manuscript's length)
Embree, Mark +2 more
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