Results 21 to 30 of about 3,479 (214)
FIVE-PRECISION GMRES-BASED ITERATIVE REFINEMENT ∗ [PDF]
, 2023 GMRES-based iterative refinement in three precisions (GMRES-IR3) uses a low precision LU factorization to accelerate the solution of a linear system without compromising numerical stability or robustness.
Amestoy, Patrick +5 more
core +1 more source
GMRES for the Differentiation Operator [PDF]
SIAM Journal on Numerical Analysis, 2009 We investigate using the gmres method with the differentiation operator. This operator is unbounded and thus does not fall into the framework of existing Krylov subspace theory. We establish conditions under which a function can be approximated by its own derivatives in a domain of the complex plane.
openaire +1 more source
A relaxed block splitting preconditioner for complex symmetric indefinite linear systems
Open Mathematics, 2018 In this paper, we propose a relaxed block splitting preconditioner for a class of complex symmetric indefinite linear systems to accelerate the convergence rate of the Krylov subspace iteration method and the relaxed preconditioner is much closer to the ...
Huang Yunying, Chen Guoliang
doaj +1 more source
Seleção Dinâmica da Dimensão do Subespaço de Krylov no Método GMRES(m) e suas Variantes
Trends in Computational and Applied Mathematics, 2006 Nesse trabalho apresentamos alguns algoritmos adaptativos do Método do Resíduo Mínimo Generalizado (GMRES) [10], um método iterativo para resolver sistemas de equações lineares com matrizes não simétricas e esparsas, o qual baseiase nos métodos de ...
T.T. Gonçalez, R.D. da Cunha
doaj +1 more source
Advances in Electrical and Electronic Engineering, 2014 The paper deals with the solution of large non-symmetric two-by-two block linear systems with a singular leading submatrix. Our algorithm consists of two levels.
Radek Kucera +4 more
doaj +1 more source
Deflated GMRES with multigrid for lattice QCD
Physics Letters B, 2020 Lattice QCD solvers encounter critical slowing down for fine lattice spacings and small quark mass. Traditional matrix eigenvalue deflation is one approach to mitigating this problem.
Travis Whyte +2 more
doaj +1 more source
Linear Algebra and its Applications, 2003 In their introduction, the authors state, ``We study an oddity: the class of problems for which the generalized minimal residual (GMRES) algorithm, when started with the initial guess \(x^{(0)}=0\) and using exact arithmetic, computes \(m\) iterates \(x^{(1)}=\cdots=x^{(m)}=0\) without making any progress at all.
Zavorin, Ilya +2 more
openaire +2 more sources
Residual-Based Simpler Block GMRES for Nonsymmetric Linear Systems with Multiple Right-Hand Sides
Advances in Mathematical Physics, 2018 We propose in this paper a residual-based simpler block GMRES method for solving a system of linear algebraic equations with multiple right-hand sides. We show that this method is mathematically equivalent to the block GMRES method and thus equivalent to
Qinghua Wu, Liang Bao, Yiqin Lin
doaj +1 more source
IGMRES method for linear systems [PDF]
Journal of Mahani Mathematical ResearchThe Index Generalized Minimal RESidual (IGMRES) algorithm is designed to compute the Drazin-inverse solution of a linear system of equations $Ax=b$, where $A$ is an arbitrary square matrix with index $\gamma$.
Faranges Kyanfar
doaj +1 more source
On a method for calculating generalized normal solutions of underdetermined linear systems [PDF]
Компьютерная оптика, 2020 The article presents a novel algorithm for calculating generalized normal solutions of underdetermined systems of linear algebraic equations based on special extended systems.
Alexander Zhdanov, Yury Sidorov
doaj +1 more source