Detection of near-singularity in Cholesky and LDLT factorizations

摘要

In sparse matrix applications it is often important to implement the Cholesky and LDLT factorization methods without pivoting in order to avoid excess fillin. We consider methods for detection of a nearly singular matrix by means of these factorizations without pivoting and demonstrate that a technique based on estimation of the smallest eigenvalue via inverse iteration will always reveal a nearly singular matrix.