The QRPS algorithm: A generalization of the QR algorithm for the singular values decomposition of rectangular matrices

作     者：Bolla, M. Tusnády, G. 

作者机构：MTA Szamitastechnikai es Automatizalasi Kutato Intezet Budapest H-1502 Kende U. 13-17 Hungary MTA Matematikai Kutató Intézet Budapest H-1364 Reáltanoda U. 13-15 Hungary 

出 版 物：《Periodica Mathematica Hungarica》 (Period Math Hung)

年 卷 期：1985年第16卷第3期

页      面：201-207页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：AMS (MOS) subject classifications (1980): Primary 65F15, Secondary 65F25 QR algorithm Singular values decomposition 

摘      要：A generalization of the QR algorithm proposed by Francis [2] for square matrices is introduced for the singular values decomposition of arbitrary rectangular matrices. Geometrically the algorithm means the subsequent orthogonalization of the image of orthonormal bases produced in the course of the iteration. Our purpose is to show how to get a series of lower triangular matrices by alternate orthogonal-upper triangular decompositions in different dimensions and to prove the convergence of this series. © 1985 Akadémiai Kiadó.