A Comparative Study of Iterative Numerical Methods for the Computation of the Square Root of Nonsingular Matrices

This paper studies various numerical methods for computing the square root of a matrix, a problem of interest in several areas of applied mathematics, such as the solution of differential equations and the analysis of dynamical systems. The work analyzes the conditions under which a matrix has a square root, and explores different techniques for its approximation, including Newton’s method, the Denman-Beavers iteration, and Pade based methods. Stability, convergence and computational efficiency are discussed for each approach. To validate the algorithms, numerical experiments implemented in MATLAB are presented using specific test matrices. The results show that some algorithms, such as the scaled Pade method, offer greater stability and faster convergence, particularly for symmetric positive definite matrices. Finally, the methods are compared in terms of the number of iterations, the accuracy achieved, and their applicability depending on the spectral properties of the matrix.