It is shown how the mid-point iterative method with cubical rate of convergence can be applied for finding the principal matrix square root. Using an identity between matrix sign function and matrix square root, we construct a variant of mid-point method which is asymptotically stable in the neighborhood of the solution. Finally, application of the presented approach is illustrated in solving a matrix differential equation.
F. Soleymani. S. Shateyi. F. Khaksar Haghani. "A Numerical Method for Computing the Principal Square Root of a Matrix." Abstr. Appl. Anal. 2014 (SI32) 1 - 7, 2014. https://doi.org/10.1155/2014/525087