English

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}
}
R2 v1 2026-06-21T16:40:21.869Z