Best-conditioned circulant preconditioners
نویسندگان
چکیده
منابع مشابه
Best Conditioned Circulant Preconditioners
In this paper, we discuss the solutions to a class of Hermitian positive deenite system Ax = b by the preconditioned conjugate gradient method with circulant preconditioner C. In general, the smaller the condition number (C ?1=2 AC ?1=2) is, the faster the convergence of the method will be. The circulant matrix C b that minimizes (C ?1=2 AC ?1=2) is called the best conditioned circulant precond...
متن کاملCirculant Preconditioners for Ill-Conditioned Hermitian Toeplitz Matrices
In this paper, we propose a new family of circulant preconditioners for solving ill-conditioned Hermitian Toeplitz systems Ax = b. The eigenval-ues of the preconditioners are given by the convolution products of the generating function f of A with some summation kernels. When f is a nonnegative 2-periodic continuous function deened on ?; ] with a zero of order 2p, we show that the circulant pre...
متن کاملThe Best Circulant Preconditioners for Hermitian Toeplitz Systems
In this paper, we propose a new family of circulant preconditioners for ill-conditioned Hermitian Toeplitz systems Ax = b. The preconditioners are constructed by con-volving the generating function f of A with the generalized Jackson kernels. For an n-by-n Toeplitz matrix A, the construction of the preconditioners only requires the entries of A and does not require the explicit knowledge of f. ...
متن کاملCirculant Preconditioners Constructed From Kernels
We consider circulant preconditioners for Hermitian Toeplitz systems from the view point of function theory. We show that some well-known circulant preconditioners can be derived from convoluting the generating function f of the Toeplitz matrix with famous kernels like the Dirichlet and the Fej er kernels. Several circulant precondition-ers are then constructed using this approach. Finally, we ...
متن کاملGeneralized circulant Strang-type preconditioners
SUMMARY Strang's proposal to use a circulant preconditioner for linear systems of equations with a Hermitian positive definite Toeplitz matrix has given rise to considerable research on circulant preconditioners. This paper presents an {e iϕ }-circulant Strang-type preconditioner.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)00171-u