A Lanczos approach to the inverse square root of a large and sparse matrix (Q1577026)

The author presents a Lanczos method to compute the inverse square root of a large and sparse positive definite matrix. The algorithm is a stable version of an earlier proposal of the author. The proposed method is characterized by a residual vector norm that decreases monotonically and by a consistent stopping condition. The ``matrix sign'' and the ``polar decomposition'' of a matrix are the concepts used in the paper. The paper has no theorems, lemmas, or propositions, but it has a descriptive character.