Implementation details of an extended oqds algorithm for singular values

Abstract

We introduce an extended oqds algorithm for singular values of lower tridiagonal matrix which is a condensed form of inputted full matrix. Reduction to the lower tridiagonal matrix is able to be performed using cache-efficient block Householder method based on BLAS 2.5 routines. In this letter, we describe the implementation details of the latter algorithm such as the shift strategy and criteria for deflation and splitting. The effectiveness of our approach is demonstrated by numerical experiments.