The Padé iterations for the matrix sign function and their reciprocals are optimal

Details The Padé iterations for the matrix sign function and their reciprocals are optimal The Padé iterations for the matrix sign function and their reciprocals are optimal

2010-11-08

arxiv.org/abs/1011.1725v2

Linear Algebra Appl. 436 (2012), no. 3, pp. 472-477

Mathematics

Numerical Analysis

Scientific paper

10.1016/j.laa.2011.04.016

It is proved that among the rational iterations locally converging with order
s>1 to the sign function, the Pad\'e iterations and their reciprocals are the
unique rationals with the lowest sum of the degrees of numerator and
denominator.

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