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矩阵加权QR分解的一阶扰动界 被引量：1

First Order Perturbation Bound for Matrix Weighted QRFactorization
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摘要 利用经典的矩阵方程方法、修正的矩阵方程方法和矩阵-向量方程方法讨论加权QR分解的扰动分析问题,得到了范数型扰动下的范数型一阶扰动界. We discussed the perturbation analysis for the weighted QR factorization by using the classical matrix equation method, the refined matrix equation method and the matrix-vector equation method, and obtained the first-order normwise perturbation bounds with normwise perturbations.
作者 吕鹏 李寒宇
机构地区 重庆大学数学与统计学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2016年第4期725-731,共7页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:11201507) 中央高校基本科研业务费专项基金(批准号:106112015CDJXY100003)
关键词 加权QR分解 范数型扰动 一阶扰动界 矩阵-向量方程方法 weighted QR factorization normwise perturbation first-order perturbation bound matrix-vector equation method
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献17

  • 1Gulliksson M, Wedin P A. Modifying the QR-Decomposition to Constrained and Weighted Linear Least Squares [J]. SIAM J Matrix Anal Appl, 1992, 13(4) : 1298-1313.
  • 2Gulliksson M. Backward Error Analysis for the Constrained and Weighted Linear Least Squares Problem When Using the Weighted QR Factorization [J]. SIAM J Matrix Anal Appl, 1995, 16(2) : 675-687.
  • 3Stewart G W. Perturbation Bounds for the QR Factorization of a Matrix[J]. SIAM J Numer Anal, 1977, 14(3) : 509-518.
  • 4SUN Jiguang. Perturbation Bounds for the Cholesky and OR Factorization[J]. BIT Numerical Mathematics, 1991, 31(2): 341-352.
  • 5ZHA Hongyuan. A Componentwise Perturbation Analysis of the QR Decomposition [J]. SIAM J Matrix Anal Appl, 1993, 14(4): 1124-1131.
  • 6CHANG Xiaowen. Perturbation Analysis of Some Matrix Factorizations [D]. Montroal.. McGill University, 1997.
  • 7CHANG Xiaowen, Paige C C, Stewart G W. Perturbation Analysis for the QR Factorization [J]. SIAM J Matrix Anal Appl, 1997, 18(3): 775-791.
  • 8CHANG Xiaowen, Paige C C. Componentwise Perturbation Analysis for the QR Factorization [J]. Numer Math, 2001, 88(2): 319-345.
  • 9CHANG Xiaowen, Stehl6 D. Rigorous Perturbation Bounds of Some Matrix Factorizations [J]. SIAM J Matrix Anal Appl, 2010, 31(5): 2841-2859.
  • 10CHANG Xiaowen, LI Rencang. Muhiplicative Perturbation Analysis for QR Factorizations [J]. Numer Algebra Control Optim, 2011, 1(2): 301-316.

同被引文献16

  • 1WANG Guorong, WEI Yimin, QIAO Sanzheng. Generalized Inverses: Theory and Computations[M]. Beijing: Science Press, 2004.
  • 2RAO C R, Mitra S K. Generalized Inverses of Matrices and its Applications[M]. New York: Wiley, 1971.
  • 3Gulliksson M, Wedin P A. Modifying the QR decomposition to weighted and constrained linear least squares[J]. SIAM J. Matrix Anal. Appl., 1992, 13: 1298-1313.
  • 4Gulliksson M. Backward error analysis for the constrained and weighted linear least squares problem when using the weighted QR factorization [J]. SIAM J. Matrix Anal. Appl., 1995, 16(2): 675-687.
  • 5Stewart G W. Perturbation bounds for the QR factorization of a matrix[J]. SIAM J. Numer. Anal., 1977, 14: 509-518.
  • 6SUN Jiguang. Perturbation bounds for the Cholesky and QR factorization[J]. BIT, 1991, 31: 341-352.
  • 7ZHA H. A componentwise perturbation analysis of the QR decomposition[J]. SIAM J. Matrix Anal. Appl., 1993, 14: 1124-1131.
  • 8CHANG Xiaowen. Perturbation Analysis of Some Matrix Factorizations[D]. Montreal: McGill Uni- versity, 1997.
  • 9CHANG Xiaowen, Paige C C, Stewart G W. Perturbation analyses for the QR factorization[J]. SIAM J. Matrix Anal. Appl., 1997, 18: 775-797.
  • 10CHANG Xiaowen, Stehl D. Rigorous perturbation bounds of some matrix factorizations[J]. SIAM J. Matrix Anal. Appl., 2010, 31: 2841-2859.

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吉林大学学报（理学版）
2016年 第4期

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