Schur-type Algorithms for the Solution of Hermitian Toeplitz Systems via Factorization
نویسندگان
چکیده
In this paper fast algorithms for the solution of systems Tu = b with a strongly nonsingular hermitian Toeplitz coefficient matrix T via different kinds of factorizations of the matrix T are discussed. The first aim is to show that ZW-factorization of T is more efficient than the corresponding LU-factorization. The second aim is to design and compare different Schurtype algorithms for LUand ZW-factorization of T . This concerns the classical Schur-Bareiss algorithm, 3-term one-step and double-step algorithms, and the Schur-type analogue of a Levinson-type algorithm of B. Krishna and H. Krishna. The latter one reduces the number of the multiplications by almost 50% compared with the classical Schur-Bareiss algorithm. Mathematics Subject Classification (2000). Primary 15A23; Secondary 65F05.
منابع مشابه
Parallel Algorithms for Toeplitz Systems
We describe some parallel algorithms for the solution of Toeplitz linear systems and Toeplitz least squares problems. First we consider the parallel implementation of the Bareiss algorithm (which is based on the classical Schur algorithm). The alternative Levinson algorithm is less suited to parallel implementation because it involves inner products. The Bareiss algorithm computes the LU factor...
متن کاملNORTH- HOLLAND High Performance Algorithms for Toeplitz and Block Toeplitz Matrices
In this paper, we present several high performance variants of the classical Schur algorithm to factor various Toeplitz matrices. For positive definite block Toeplitz matrices, we show how hyperbolic Householder transformations may be blocked to yield a block Schur algorithm. This algorithm uses BLAS3 primitives and makes efficient use of a memory hierarchy. We present three algorithms for inde...
متن کاملA Block Toeplitz Look - Ahead Schur
This paper gives a look-ahead Schur algorithm for nding the symmetric factorization of a Hermitian block Toeplitz matrix. The method is based on matrix operations and does not require any relations with orthogonal polynomials. The simplicity of the matrix based approach ought to shed new light on other issues such as parallelism and numerical stability.
متن کاملOn Solving Block Toeplitz Systems Using a Block Schur Algorithm
This paper presents a block Schur algorithm to obtain a factorization of a symmetric block Toeplitz matrix. It is inspired by the various block Schur algorithms that have appeared in the literature but which have not considered the innuence of performance tradeoos on implementation choices. We develop a version based on block hyperbolic Householder reeectors by adapting the representation schem...
متن کاملAlgorithms for rank-de cient and ill-conditioned Toeplitz least-squares and QR factorization
In this paper we present two algorithms-one to compute the QR factorization of nearly rank-deecient Toeplitz and block Toeplitz matrices and the other to compute the solution of a severely ill-conditioned Toeplitz least-squares problem. The rst algorithm is based on adapting the generalized Schur algorithm to Cauchy-like matrices and has some rank-revealing capability. The other algorithm is ba...
متن کامل