Circulant and skew-circulant splitting methods for Toeplitz systems
نویسندگان
چکیده
منابع مشابه
Accelerated Circulant and Skew Circulant Splitting Methods for Hermitian Positive Definite Toeplitz Systems
We study the CSCS method for large Hermitian positive definite Toeplitz linear systems, which first appears in Ng’s paper published in Ng, 2003 , and CSCS stands for circulant and skew circulant splitting of the coefficient matrix A. In this paper, we present a new iteration method for the numerical solution of Hermitian positive definite Toeplitz systems of linear equations. The method is a tw...
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We study the solutions of Hermitian positive deenite Toeplitz systems Ax = b by the preconditioned conjugate gradient method for three families of circulant preconditioners C. The convergence rates of these iterative methods depend on the spectrum of C ?1 A. For a Toeplitz matrix A with entries which are Fourier coeecients of a positive function f in the Wiener class, we establish the invertibl...
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Preconditioned conjugate gradient method is used to solve n-by-n Hermitian Toeplitz systems A n x = b. The preconditioner S n is the Strang's circulant preconditioner which is deened to be the circulant matrix that copies the central diagonals of A n. The convergence rate of the method depends on the spectrum of S ?1 n A n. Using Jackson's theorem in approximation theory, we prove that if A n h...
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t 0 t −1 t −2 · · · t −(n−1) t 1 t 0 t −1 t 2 t 1 t 0. .. t n−1 · · · t 0 The fundamental theorems on the asymptotic behavior of eigenval-ues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(03)00562-4