Given an n -by- n nonsingular matrix A, the solution to X 2 A = I is called an inverse square root of A and is denoted by X = A - 1&slash;2. The inverse square root of a matrix is relevant to finding an optimal symmetric orthogonalization of a set of vectors in matrix theory. Computational methods for finding the square root of a matrix have been studied by various authors, including Higham [1]. This paper considers the inverse square root.
Two iterative techniques are suggested for computing the inverse square root, A - 1&slash;2, of A. Each approach involves an application of Newton’s method to the matrix equation F ( X ) = ( XA ) - 1 - X = 0. The two schemes are analyzed and their numerical properties are discussed. Some small numerical examples are also provided.
