An algorithm for computing matrix square roots with application to Riccati equation implementation

An iterative algorithm is presented for obtaining a positive definite symmetric square root of a positive definite symmetric matrix. This algorithm has application in the implementation of Riccati type equations. The approach presented here has the advantage that apriori upper and lower bounds to the converged answer can be obtained sequentially at any point in the iterative process. These apriori bounds can also be obtained for the Riccati equation using a discrete implementation procedure. Theorems on convergence are proved and examples are worked.