Results 61 to 70 of about 4,826 (176)

Solution of Linear Systems by GMRES Method on Global Computing Platform

Journal of Algorithms & Computational Technology, 2007
By making use of a very large amount of unexploited computing resources, grid computing achieves high throughput computing. We present a classical parallel method GMRES (m) to solve large sparse linear systems utilizing a lightweight GRID system XtremWeb.
Haiwu He, Guy Bergere, Zhijian Wang, Serge Petiton   +3 more
doaj   +1 more source

Exploiting variable precision in GMRES

CoRR, 2019
We describe how variable precision floating point arithmetic can be used in the iterative solver GMRES. We show how the precision of the inner products carried out in the algorithm can be reduced as the iterations proceed, without affecting the convergence rate or final accuracy achieved by the iterates.
Serge Gratton, Ehouarn Simon, David Titley-Péloquin, Philippe L. Toint   +3 more
openaire   +4 more sources

GMRES on singular systems revisited

CoRR, 2020
In [Hayami K, Sugihara M. Numer Linear Algebra Appl. 2011; 18:449--469], the authors analyzed the convergence behaviour of the Generalized Minimal Residual (GMRES) method for the least squares problem $ \min_{ {\bf x} \in {\bf R}^n} {\| {\bf b} - A {\bf x} \|_2}^2$, where $ A \in {\bf R}^{n \times n}$ may be singular and $ {\bf b} \in {\bf R}^n$, by ...
Ken Hayami, Kota Sugihara
openaire   +2 more sources

Nonlinear Heat Diffusion Problem Solution with Spatio-Temporal Constraints Based on Regularized Gauss–Newton and Preconditioned Krylov Subspaces

Eng
In this work, we proposed a dynamic inverse solution with spatio-temporal constraints of the nonlinear heat diffusion problem in 1D and 2D based on a regularized Gauss–Newton and Krylov subspace with a preconditioner.
Luis Fernando Alvarez-Velasquez, Eduardo Giraldo   +1 more
doaj   +1 more source

More on Generalizations and Modifications of Iterative Methods for Solving Large Sparse Indefinite Linear Systems

Journal of Applied Mathematics, 2014
Continuing from the works of Li et al. (2014), Li (2007), and Kincaid et al. (2000), we present more generalizations and modifications of iterative methods for solving large sparse symmetric and nonsymmetric indefinite systems of linear equations.
Jen-Yuan Chen, David R. Kincaid, Yu-Chien Li   +2 more
doaj   +1 more source

Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation

پژوهش‌های ریاضی, 2019
Introduction Fractional differential equations (FDEs)  have  attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc.
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doaj  

Adaptive metric-based multigrid for a Poisson problem with discontinuous coefficients*, **

ESAIM: Proceedings and Surveys, 2014
In order to solve the linear partial differential equation Au = f, we combine two methods: Full-Multigrid method and Hessian-based mesh adaptation.
Brèthes Gautier
doaj   +1 more source

Mixed Precision Augmented GMRES

We aim to accelerate the restarted generalized minimal residual (GMRES) method for the solutions of linear systems by combining two types of techniques. On the one hand, mixed precision GMRES algorithms, which use lower precision in certain steps of the ...
Pierre Jolivet, Yongseok Jang, Théo Mary   +2 more
core   +2 more sources

Heavy Ball Restarted CMRH Methods for Linear Systems

Mathematical and Computational Applications, 2018
The restarted CMRH method (changing minimal residual method based on the Hessenberg process) using fewer operations and storage is an alternative method to the restarted generalized minimal residual method (GMRES) method for linear systems.
Zhongming Teng, Xuansheng Wang
doaj   +1 more source

Evaluation of the performance of inexact GMRES

Journal of Computational and Applied Mathematics, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Roger B. Sidje, Nathan Winkles
openaire   +1 more source