Fast enclosure for a matrix inverse square root - Miyajima, Shinya (Linear algebra and its applications, 2015)
A fast algorithm for computing an interval matrix containing the inverse square root of an n×n matrix A is proposed. This algorithm utilizes numerical spectral decomposition of A and requires only O(n3) operations. The principal property and uniqueness of the contained inverse square root can moreover be verified by the proposed algorithm. Numerical results show the effectiveness and efficiency of this algorithm.