Superlinear PCG methods for symmetric Toeplitz systems
نویسندگان
چکیده
منابع مشابه
Superlinear PCG methods for symmetric Toeplitz systems
In this paper we deal with the solution, by means of preconditioned conjugate gradient (PCG) methods, of n × n symmetric Toeplitz systems An(f)x = b with nonnegative generating function f . Here the function f is assumed to be continuous and strictly positive, or is assumed to have isolated zeros of even order. In the first case we use as preconditioner the natural and the optimal τ approximati...
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In this paper we deal with the solution, by means of preconditioned conjugate gradient (PCG) methods, of n × n symmetric Toeplitz systems An(f)x = b with nonnegative generating function f . Here the function f is assumed to be continuous and strictly positive, or is assumed to have isolated zeros of even order. In the first case we use as preconditioner the natural and the optimal τ approximati...
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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...
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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...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1999
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-99-01045-5