Clusters, preconditioners, convergence
نویسندگان
چکیده
منابع مشابه
Some Convergence Estimates For Algebraic Multilevel Preconditioners
We discuss the construction of algebraic multilevel preconditioners for the conjugate gradient method and derive explicit and sharp bounds for the convergence rates. We present several numerical examples that demonstrate the efficiency of the preconditioner. sparse approximate inverse, sparse matrix, algebraic multilevel method, preconditioning, conjugate gradient method, Krylov subspace method...
متن کاملSuperlinear Convergence for PCG Method using Algebra plus Band Preconditioners
This paper concerns on the fast and efficient solution of n × n symmetric ill conditioned Toeplitz systems T n (f)x = b, where the generating function f is a priori known, nonnegative real valued, having isolated roots of even order. The preconditioner setting that we propose is a product of a band Toeplitz matrix and matrices that belong to any trigonometric algebra. The proposed scheme tries ...
متن کاملSuperlinear convergence for PCG using band plus algebra preconditioners for Toeplitz systems
The paper studies fast and efficient solution algorithms for n× n symmetric ill conditioned Toeplitz systems Tn(f )x = bwhere the generating function f is known a priori, real valued, nonnegative, and has isolated roots of even order. The preconditioner that we propose is a product of a band Toeplitz matrix and matrices that belong to a certain trigonometric algebra. The basic idea behind the p...
متن کاملMatrix algebra preconditioners for multilevel Toeplitz systems do not insure optimal convergence rate
In the last decades several matrix algebra optimal and superlinear preconditioners (those assuring a strong clustering at the unity) have been proposed for the solution of polynomially ill-conditioned Toeplitz linear systems. The corresponding generalizations for multilevel structures are neither optimal nor superlinear (see e.g. Contemp. Math. 281 (2001) 193). Concerning the notion of superlin...
متن کاملField-of-Values Convergence Analysis of Augmented Lagrangian Preconditioners for the Linearized Navier-Stokes Problem
We study a block triangular preconditioner for finite element approximations of the linearized Navier–Stokes equations. The preconditioner is based on the augmented Lagrangian formulation of the problem and was introduced by the authors in [SIAM J. Sci. Comput., 28 (2006), pp. 2095–2113]. In this paper we prove field-of-values type estimates for the preconditioned system which lead to optimal c...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(96)00445-4