On high relative accuracy of the Kogbetliantz method

The relative accuracy of the Kogbetliantz method for computing the singular value decomposition of real triangular matrices is considered. Sharp relative error bounds for the computed singular values are derived. The results are obtained by estimating the norms of scaled perturbation matrices arising from errors generated in one step and one batch of commuting transformations. Perturbation matrices are scaled either from the left or right side by the inverse of the diagonal matrix.