Preconditioned conjugate gradients, radial basis functions, and Toeplitz matrices
نویسندگان
چکیده
منابع مشابه
A Preconditioned MINRES Method for Nonsymmetric Toeplitz Matrices
Circulant preconditioners that cluster eigenvalues are well established for linear systems involving symmetric positive definite Toeplitz matrices. For these preconditioners rapid convergence of the preconditioned conjugate gradient method is guaranteed. Since circulant preconditioners can be applied quickly using the fast Fourier transform, preconditioned CG with circulant preconditioning is e...
متن کاملAsymptotic Results on the Spectra of Block Toeplitz Preconditioned Matrices
It is well known that the generating function f ∈ L([−π, π],R) of a class of Hermitian Toeplitz matrices An(f) describes very precisely the spectrum of each matrix of the class [U. Grenader and G. Szegö, Toeplitz Forms and Their Applications, 2nd ed., Chelsea, New York, 1984; E. E. Tyrtyshnikov, Linear Algebra Appl., 232 (1996), pp. 1–43]. In this paper we consider n×n block Toeplitz matrices w...
متن کاملParallel Preconditioned Conjugate-Gradients Methods on Transputer Networks
We show how highly efficient parallel implementations of basic linear algebra routines may be used as building blocks to implement efficient higher level algorithms. We discuss the solution of systems of linear equations using a preconditioned Conjugate-Gradients iterative method on a network of transputers. Results are presented for the solution of both dense and sparse systems; the latter bei...
متن کاملSpectral Functions for Real Symmetric Toeplitz Matrices
We derive separate spectral functions for the even and odd spectra of a real symmetric Toeplitz matrix, which are given by the roots of those functions. These are rational functions, also commonly referred to as secular functions. Two applications are considered: spectral evolution as a function of one parameter and the computation of eigenvalues.
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2002
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(01)00288-7