The Padé iterations for the matrix sign function and their reciprocals are optimal
arXiv:1011.1725 · doi:10.1016/j.laa.2011.04.016
Abstract
It is proved that among the rational iterations locally converging with order s>1 to the sign function, the Padé iterations and their reciprocals are the unique rationals with the lowest sum of the degrees of numerator and denominator.