A Kogbetliantz-type algorithm for the hyperbolic SVD

In this paper, a two-sided, parallel Kogbetliantz-type algorithm for the hyperbolic singular value decomposition (HSVD) of real and complex square matrices is developed, with single assumption that input matrix, order n, admits such into product unitary, non-negative diagonal, J-unitary where J given diagonal matrix positive negative signs. When = ±I, proposed computes ordinary SVD. The paper’s most important contribution—a derivation formulas HSVD 2 × matrices—is presented first, followed by details their implementation in floating-point arithmetic. Next, effects transformations on columns iteration are discussed. These then guide redesign dynamic pivot ordering, being already well-established strategy Kogbetliantz algorithm, general, n HSVD. A heuristic but sound convergence criterion proposed, which contributes to high accuracy demonstrated numerical testing results. Such J-Kogbetliantz as here intrinsically slow, nevertheless usable small orders.