Accuracy of the Kogbetliantz method for scaled diagonally dominant triangular matrices

摘要

The paper proves that Kogbetliantz method computes all singular values of a scaled diagonally dominant triangular matrix, which can be well scaled from both sides symmetrically, to high relative accuracy. Special attention is paid to deriving sharp accuracy bounds for one step, one batch and one sweep of the method. By a simple numerical test it is shown that the methods based on bidiagonalization are generally not accurate on that class of well-behaved matrices.