Results 11 to 20 of about 753 (179)
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.
Carl T. Kelley, Z. Q. Xue
openaire +2 more sources
Multipreconditioned Gmres for Shifted Systems [PDF]
SIAM Journal on Scientific Computing, 2017 An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix.
Tania Bakhos +4 more
openaire +5 more sources
Adaptive version of Simpler GMRES [PDF]
Numerical Algorithms, 2009 The authors propose and theoretically analyze a stable version of simpler generalized minimal residual (GMRES) algorithm, based on an adaptive choice of the Krylov subspace basis at a given iteration step. They show that this adaptive choice of direction vectors keeps the basis well-conditioned and that the condition number grows at most linearly with ...
Pavel Jiránek, Miroslav Rozlozník
openaire +2 more sources
SIAM Journal on Scientific Computing, 2023 The GMRES algorithm of Saad and Schultz (1986) is an iterative method for approximately solving linear systems $A{\bf x}={\bf b}$, with initial guess ${\bf x}_0$ and residual ${\bf r}_0 = {\bf b} - A{\bf x}_0$. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of $V_k$).
Stephen J. Thomas +4 more
openaire +5 more sources
Properties of Worst-Case GMRES [PDF]
SIAM Journal on Matrix Analysis and Applications, 2013 In the convergence analysis of the GMRES method for a given matrix $A$, one quantity of interest is the largest possible residual norm that can be attained, at a given iteration step $k$, over all unit norm initial vectors. This quantity is called the worst-case GMRES residual norm for $A$ and $k$.
Vance Faber, Jörg Liesen, Petr Tichý
openaire +4 more sources
DAPHNE-3D: A NEW TRANSPORT SOLVER FOR UNSTRUCTURED TETRAHEDRAL MESHES [PDF]
EPJ Web of Conferences, 2021 A new Discrete Ordinates transport solver for unstructured tetrahedral meshes is presented. The solver uses the Discontinuous Galërkin Finite Element Method with linear or quadratic expansion of the flux within each cell.
Diamantopoulou Evangelia +1 more
doaj +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
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 +2 more sources
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