Scaled Fixed Point Algorithm for Computing the Matrix Square Root

02/18/2020

∙

by   Harry F. Oviedo, et al.

∙

0

∙

share

This paper addresses the numerical solution of the matrix square root problem. Two fixed point iterations are proposed by rearranging the nonlinear matrix equation A - X^2 = 0 and incorporating a positive scaling parameter. The proposals only need to compute one matrix inverse and at most two matrix multiplications per iteration. A global convergence result is established. The numerical comparisons versus some existing methods from the literature, on several test problems, demonstrate the efficiency and effectiveness of our proposals.