Effective methods for solving banded Toeplitz systems

被引：48

作者：

Bini, DA ^{[1
]}

Meini, B ^{[1
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1999年 / 20卷 / 03期

关键词：

banded matrices; Toeplitz matrices; displacement rank; cyclic reduction; Graeffe's method;

D O I：

10.1137/S0895479897324585

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose new algorithms for solving n x n banded Toeplitz systems with bandwidth m. If the function associated with the Toeplitz matrix has no zero in the unit circle, then O(n log m+ m log(2) m log log epsilon(-1)) arithmetic operations (ops) are sufficient to approximate the solution of the system up to within the error epsilon; otherwise the cost becomes O(n log m + m log(2) m log n/m) ops. Here m = o(n) and n > log epsilon(-1). Some applications are presented. The methods can be applied to infinite and bi-infinite systems and to block matrices.

引用

页码：700 / 719

页数：20