Linear convergence of the row cyclic Jacobi and Kogbetliantz methods
The Kogbetliantz method (KM) [cf. \textit{E. Kogbetliantz}, Quart. Appl. Math. 13, 123-132 (1955; Zbl 0066.101)] for computing the singular value decomposition of a matrix is studied. It is indicated how to achieve global convergence of KM by restricting the rotations to certain domains. For triangular matrices, this requires certain constraints concerning the angles of rotations. It is also indicated how this problem can be removed by using a modified cyclic method which was originally proposed by W. M. Gentleman. The author has also extended this analysis to square matrices and proposed a scheme which guarantees global convergence without under- rotations.
scientific article; zbMATH DE number 4117743
scientific article