The Binomial Method for a Matrix Square Root

Abstract

Abstract. There are various methods for evaluating a matrix square root, which is a solvent of the quadratic matrix equation X 2 − A = 0. We consider new iterative methods for solving matrix square roots of Mmatrices. Particulary we show that the relaxed binomial iteration is more efficient than Newton-Schulz iteration in some cases. And we construct a formula to find relaxation coefficients through statistical experiments.