Matrix algebra preconditioners for multilevel Toeplitz systems do not insure optimal convergence rate

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Matrix 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 کامل

Multigrid Optimal Convergence for Multilevel Matrix Algebra Linear Systems

We present a multigrid algorithm to solve linear sistems whose coefficient metrices belongs to circulant, Hartley or τ multilevel algebras and are generated by a nonnegative multivariate polinomial f . It is known that these matrices are banded (with respect to their multilevel structure) and their eigenvalues are obtained by sampling f on uniform meshes, so they are ill-conditioned (or singula...

متن کامل

Superlinear 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 کامل

Inverse Toeplitz preconditioners for Hermitian Toeplitz systems

In this paper we consider solving Hermitian Toeplitz systems Tnx= b by using the preconditioned conjugate gradient (PCG) method. Here the Toeplitz matrices Tn are assumed to be generated by a non-negative continuous 2 -periodic function f, i.e. Tn =Tn[f]. It was proved in (Linear Algebra Appl. 1993; 190:181) that if f is positive then the spectrum of Tn[1=f]Tn[f] is clustered around 1. We prove...

متن کامل

Optimal, Quasi–optimal and Superlinear Band–toeplitz Preconditioners for Asymptotically Ill–conditioned Positive Definite Toeplitz Systems

In this paper we are concerned with the solution of n × n Hermitian Toeplitz systems with nonnegative generating functions f . The preconditioned conjugate gradient (PCG) method with the well–known circulant preconditioners fails in the case where f has zeros. In this paper we consider as preconditioners band–Toeplitz matrices generated by trigonometric polynomials g of fixed degree l. We use d...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Theoretical Computer Science

سال: 2004

ISSN: 0304-3975

DOI: 10.1016/j.tcs.2004.01.007