Stability of methods for solving Toeplitz systems of equations. (English) Zbl 0569.65019

Bunch, James R.

SIAM J. Sci. Stat. Comput. 6, 349-364 (1985).

The numerical stability of the known algorithms for solving Toeplitz systems of linear equations is discussed. It is shown that the classical Trench method and its variants are stable for positive definite matrices and unstable otherwise unless pivoting is used. (However, pivoting can destroy the Toeplitz structure.) The ”fast” algorithms of Bitmead- Anderson and Brent-Gustavson-Yan are also unstable for nonsymmetric and symmetric indefinite Toeplitz systems.

Reviewer: Petko Hr. Petkov

MSC:

65F05	Direct numerical methods for linear systems and matrix inversion
65F35	Numerical computation of matrix norms, conditioning, scaling

Keywords:

numerical stability; Toeplitz systems; Trench method; pivoting; Bitmead- Anderson; Brent-Gustavson-Yan