Calculation of the square root of a positive-definite matrix (Q1335706)

Algorithms for finding the square root of a positive definite matrix are examined. The first one involves inversion of matrices. While the second one does not, which, of course, speaks favorably of the accuracy of the result. The third algorithm in a certain sense combines the ideas of the first two. As a possible application of these algorithms, we may particularly mention problems of ellipsoidal approximation, which involve numerical integration of nonlinear matrix differential equations containing the square root of the matrix sought.