Numerical methods for approximation of square roots of positive definite matrices in matrix-vector products

Two numerical methods are developed for calculating the product of the square root of a matrix with a vector, given the matrix and vector, where the matrix is positive definite. Modified forms of Newton's method and Eulers method are developed and analyzed. The methods are applicable, for example, in approximating solutions of stochastic differential equations. An analysis of Newton's method shows that the method is quadratically convergent. Numerical results indicate that the two methods are accurate and computationally fast.