C. G. preconditioning for Toeplitz matrices
نویسندگان
چکیده
منابع مشابه
Multigrid Preconditioning and Toeplitz Matrices
In this paper we discuss Multigrid methods for Toeplitz matrices. Then the restriction and prolongation operator can be seen as projected Toeplitz matrices. Because of the intimate connection between such matrices and trigonometric series we can express the Multigrid algorithm in terms of the underlying functions with special zeroes. This shows how to choose the prolongation/restriction operato...
متن کاملFast superoptimal preconditioning of multiindex Toeplitz matrices
In this article three well-known methods of circulant preconditioning of finite multiindex Toeplitz linear systems, that is linear systems indexed by integers i1, . . ., id with 0 is < ns (s = 1, . . ., d), are studied in detail. A general algorithm for the construction of the so-called superoptimal preconditioner is also given and it is shown that this procedure requires O(n1 · · · nd log(n1 ·...
متن کاملUsing ω-circulant matrices for the preconditioning of Toeplitz systems
Toeplitz systems can be solved efficiently by using iterative methods such as the conjugate gradient algorithm. If a suitable preconditioner is used, the overall cost of the method is O(n logn) arithmetic operations. Circulant matrices are frequently employed for the preconditioning of Toeplitz systems. They can be chosen as preconditioners themselves, or they can be used for the computation of...
متن کاملTwo-level Toeplitz preconditioning: approximation results for matrices and functions
Large 2-level Toeplitz systems arise in a variety of applications whose solution requires efficient numerical methods. Many of the known successful numerical techniques need the explicit knowledge of the generating function f of the considered system Tn(f)x = b, an assumption that usually in real applications like Markov chains, image processing, tomography etc is not fulfilled. In this talk, w...
متن کاملToeplitz matrices: spectral properties and preconditioning in the CG method
We consider multilevel Toeplitz matrices Tn(f) generated by Lebesgue integrable functionsf defined over I, I = [−π, π), d ≥ 1. We are interested in the solution of linear systems withcoefficient matrix Tn(f) when the size of Tn(f) is large. Therefore the use of iterative methodsis recommended for computational and numerical stability reasons. In this note we focus ourattenti...
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: Computers & Mathematics with Applications
سال: 1993
ISSN: 0898-1221
DOI: 10.1016/0898-1221(93)90297-9