A PADE-APPROXIMATION METHOD FOR SQUARE ROOTS OF SYMMETRICAL POSITIVE-DEFINITE MATRICES

A numerical method for computing the square root of a symmetric positi ve definite matrix is developed in this paper. It is based on the Pade approximation of root 1 + x in the prime fraction form. A precise ana lysis allows us to determine the minimum number of terms required in t he Pade approximation for a given error tolerance. Theoretical studies and numerical experiments indicate that the method is more efficient than the standard method based on the spectral decomposition, unless t he condition number is very large.