Rational iterative methods for the matrix sign function. (English) Zbl 0725.65048

Kenney, Charles; Laub, Alan J.

SIAM J. Matrix Anal. Appl. 12, No. 2, 273-291 (1991).

The paper presents an analysis of rational recursions for the computation of the matrix sign function, including Padé, Laurent, Cayley transform and eigenvalue assignment methods. The analysis is based on the Padé approximation of a certain hypergeometric function. It is shown that the diagonal Padé recursions are globally convergent. Graphical approximations of the regions of convergence for non-diagonal Padé recursions are plotted.

Reviewer: A.Varga (Bucureşti)

MSC:

65F30	Other matrix algorithms (MSC2010)
65F10	Iterative numerical methods for linear systems
15A24	Matrix equations and identities

Keywords:

rational iterative methods; rate of convergence; Riccati equation; rational recursions; matrix sign function; Padé approximation; regions of convergence