Toeplitz preconditioners for Hermitian Toeplitz systems
نویسندگان
چکیده
منابع مشابه
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 کاملFast Band-Toeplitz Preconditioners for Hermitian Toeplitz Systems
We consider the solutions of Hermitian Toeplitz systems where the Toeplitz matrices are generated by nonnegative functions f. The preconditioned conjugate gradient method with well-known circulant preconditioners fails in the case when f has zeros. In this paper, we employ Toeplitz matrices of xed band-width as preconditioners. Their generating functions g are trigonometric poly-nomials of xed ...
متن کاملPreconditioners for Nondefinite Hermitian Toeplitz Systems
This paper is concerned with the construction of circulant preconditioners for Toeplitz systems arising from a piecewise continuous generating function with sign changes. If the generating function is given, we prove that for any c > 0, only O(log N) eigenvalues of our preconditioned Toeplitz systems of size N xN are not contained in [-1c, -1+c]U [1-c, 1+c). The result can be modified for trigo...
متن کاملPreconditioners for Non-hermitian Toeplitz Systems 1
In this paper, we construct new !-circulant preconditioners for non-Hermitian Toeplitz systems, where we allow the generating function of the sequence of Toeplitz matrices to have zeros on the unit circle. We prove that the eigenvalues of the preconditioned normal equation are clustered at 1 and that for (N; N)-Toeplitz matrices with spectral condition number O(N) the corresponding PCG method r...
متن کاملCirculant Preconditioners for Hermitian Toeplitz Systems
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...
متن کاملذخیره 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: Linear Algebra and its Applications
سال: 1993
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)90226-e