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

MSC:
65F30Other matrix algorithms
65F10Iterative methods for linear systems
15A24Matrix equations and identities
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