Accurate Singular Values with dqds
O. A. Marques
Lawrence Berkeley National Laboratory, Berkeley, CA
Joint work with Prof. B. N. Parlett
Abstract: LAPACK now uses the dqds algorithm to compute all the singular values of a bidiagonal matrix to high relative accuracy. Singular vectors are not computed. On the LAPACK test bed it is 2.75 times faster in average than the Demmel/Kahan QR algorithm and 35% slower than Pal-Walker-Kahan (PWK) for eigenvalues of a positive definite tridiagonal on a Sun Ultra 30 workstation. However, PWK does not deliver high relative accuracy. We describe the main features of our implementation of the dqds algorithm, such as the IEEE and non IEEE versions of the code, splitting criterion and shift strategy. We also describe the difficulties raised by underflow.