The Pad\'e iterations for the matrix sign function and their reciprocals are optimal
Numerical Analysis
2011-11-15 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1011.1725,
title = {The Pad\'e iterations for the matrix sign function and their reciprocals are optimal},
author = {Federico Greco and Bruno Iannazzo and Federico Poloni},
journal= {arXiv preprint arXiv:1011.1725},
year = {2011}
}