Lanczos Approach to the Inverse Square Root of a Large and Sparse Matrix

I construct a Lanczos process on a large and sparse matrix and use the results of this iteration to compute the inverse square root of the same matrix. The algorithm is a stable version of an earlier proposal by the author. It can be used for problems related to the matrix sign and polar decomposition. The application here comes from the theory of chiral fermions on the lattice.