In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to … See more Denote the Euclidean norm of any vector v by $${\displaystyle \ v\ }$$. Denote the (square) system of linear equations to be solved by $${\displaystyle Ax=b.\,}$$ The matrix A is … See more The Arnoldi iteration reduces to the Lanczos iteration for symmetric matrices. The corresponding Krylov subspace method is the minimal residual method (MinRes) of Paige … See more One part of the GMRES method is to find the vector $${\displaystyle y_{n}}$$ which minimizes $${\displaystyle \ {\tilde {H}}_{n}y_{n}-\beta e_{1}\ .\,}$$ Note that $${\displaystyle {\tilde {H}}_{n}}$$ is an (n + 1)-by-n … See more The nth iterate minimizes the residual in the Krylov subspace $${\displaystyle K_{n}}$$. Since every subspace is contained in the next subspace, the residual does not … See more Like other iterative methods, GMRES is usually combined with a preconditioning method in order to speed up convergence. The cost of the iterations grow as O(n ), where n is the iteration number. Therefore, the method is sometimes restarted after a number, say k, of … See more • Biconjugate gradient method See more • A. Meister, Numerik linearer Gleichungssysteme, 2nd edition, Vieweg 2005, ISBN 978-3-528-13135-7. • Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, Society for Industrial and Applied Mathematics, 2003. ISBN 978-0-89871-534-7 See more Webgeneralized minimal residual (GMRES) method [2] and its variant flexible GMRES (FGMRES) [3] are popular options due to their robustness and smooth convergence, see [4]. In terms of cheaper memory demanding, some of the short-recurrence methods based on Bi-Lanczos process are effective and competitive.
A New Type of Variable Preconditioning for a Generalized Minimum ...
WebIn this article, a local coupling multitrace domain decomposition method (LCMT-DDM) based on surface integral equation ... Since the subdomain matrices are diagonally dominant, the flexible generalized minimal residual (FGMRES) technique is used to accelerate the iterative solution of the whole DDM system. Moreover, an effective … WebAug 9, 2024 · Different numerical integral algorithms are discussed for solving the rigid-flexible cable system and an integration strategy which combines Implicit Euler with Minimum Residual Method (MINRES) is ... ayme savoie
Robust preconditioning for a mixed formulation of phase-field …
WebFlexible methods refer to a class of methods where the preconditioner is allowed to vary at each iteration. We refer the reader to e.g. [29] for a general introduction on Krylov subspace methods and to [29, Section 10] and [25, Section 9.4] for a review on flexible methods. The minimum residual norm GMRES method [26] has been extended by Saad ... WebOct 1, 2011 · First we recall the main features of flexible generalized minimum residual with deflated restarting (FGMRES-DR), a recently proposed algorithm of the same family but based on the GMRES method. ayn loki console