Sensitivity analysis for the symplectic QR factorization

Abstract In this paper, we give the sensitivity analysis for an implicit Bunch form of the symplectic QR factorization. In particular, we present some new first order normwise perturbation bounds for R - and Q -factors and propose the normwise condition numbers appropriately for two factors. Some numerical examples are given to demonstrate the theoretical results.

[1]  G. Stewart,et al.  Perturbation Analyses for the QR Factorization , 1997, SIAM J. Matrix Anal. Appl..

[2]  Wen Li,et al.  Sensitivity analysis for the SR decomposition , 2015 .

[3]  Hua Xiang,et al.  Structured mixed and componentwise condition numbers of some structured matrices , 2007 .

[4]  Yimin Wei,et al.  On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems , 2006, Math. Comput..

[5]  Rounding error and perturbation bounds for the symplectic QR factorization , 2003 .

[6]  Hu Yang,et al.  Perturbation analysis for the symplectic QR factorization , 2015 .

[7]  James R. Bunch,et al.  A note on the stable decompostion of skew-symmetric matrices , 1982 .

[8]  A. Bunse-Gerstner.  Matrix factorizations for symplectic QR-like methods , 1986 .

[9]  J. Rice.  A Theory of Condition , 1966 .

[10]  Yimin Wei,et al.  On condition numbers for Moore–Penrose inverse and linear least squares problem involving Kronecker products , 2013, Numer. Linear Algebra Appl..

[11]  Xiao-Qing Jin,et al.  On condition numbers for the canonical generalized polar decompostion of real matrices , 2013 .

[12]  R. Bhatia.  Matrix factorizations and their perturbations , 1994 .

[13]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[14]  Xiao-Wen Chang,et al.  On the sensitivity of the SR decomposition , 1998 .

[15]  A. Bunse-Gerstner,et al.  A symplectic QR like algorithm for the solution of the real algebraic Riccati equation , 1986 .