We provide sufficient conditions for the general sequential block Jacobi-type method to
converge to the diagonal form for cyclic pivot strategies which are weakly equivalent to the …

A new algorithm for the accurate computation of the singular value decomposition of 2× 2
triangular matrices is proposed. The algorithm is based on Voevodin formulas. Sharp …

Recently, Drmac and Veselic [8],[9] have modified the one-sided Jacobi method for
computing the singular value decomposition (SVD) of general matrices. Their modification is …

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 …

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 …

This paper estimates the quadratic convergence reduction of scaled iterates by J-symmetric
Jacobi method [Numer. Math. 64 (1993) 241]. Although, the method is well defined for a …

The paper derives improved relative perturbation bounds for the eigenvalues of scaled
diagonally dominant Hermitian matrices and new relative perturbation bounds for the …

Abstract Using the technique from [12], sharp quadratic convergence bounds for scaled
Jacobi iterates are derived. The iterates are generated by any serial Jacobi method when …

Using a fine accuracy analysis and the results from [9], a new accurate algorithm for
computing the singular value decomposition of 2 by 2 triangular matrices is constructed. It is …

Recently, Drmac and Veselic [8, 9] have modified the one-sided Jacobi method for
computing the singular value decomposition (SVD) of general matrices, to become faster …