Un método simplificado de newton para calcular la raíz cuadrada de una matriz real simétrica definida positiva

Abstract

One of the numerically stable methods to calculate he Squire root of a matrix is the Newton’s Method, but it has the disadvantage that in each iteration it is necessary to solve a Sylvester’s matrix equation for full matrix, which is computationally expensive. Modifications to the method have been made, resulting a pair of simplified iterations, but it has been proved, through the perturbations theory, that these are numerically unstable. In this article, a simplified alternative iteration of Newton’s Method for the calculation of the square root of a positive definite real matrix is presented, which is attractive for being convergent, computationally economic and, for practical purposes, numerically stable.

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