|Table of Contents|

[1] Li Xinxiu, Nie Xiaobing,. Rice condition numbers of QR and Cholesky factorizations [J]. Journal of Southeast University (English Edition), 2004, 20 (1): 130-134. [doi:10.3969/j.issn.1003-7985.2004.01.027]
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Rice condition numbers of QR and Cholesky factorizations()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
20
Issue:
2004 1
Page:
130-134
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2004-03-30

Info

Title:
Rice condition numbers of QR and Cholesky factorizations
Author(s):
Li Xinxiu1;  Nie Xiaobing2
1Department of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
Keywords:
Rice condition number;  Cholesky factorization;  QR decomposition
PACS:
O241.6
DOI:
10.3969/j.issn.1003-7985.2004.01.027
Abstract:
A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition numbers are defined for factors of some matrix factorizations such as the Cholesky factorization of a symmetric positive definite matrix and QR factorization of a general matrix. The condition numbers are derived by a technique of analytic expansion of the factor dependent on one parameter and matrix-vector equation. Condition numbers of the Cholesky and QR factors are different from the ones previously introduced by other authors, but similar to Chang’s results. In Cholesky factorization, corresponding with the condition number of the factor matrix L, KL is a low bound of Stewart’s condition number K.

References:

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[4] Stewart G W. On the perturbation of LU, Cholesky and QR factorizations [J]. SIAM J Matrix Anal Appl, 1993, 14: 1141-1145.
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[7] Chang Xiaowen, Paige C C. Sensitivity analysis for factorizations of sparse or structured matrices [J]. Lin Alg Appl, 1998284: 53-72.
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Memo

Memo:
Biography: Li Xinxiu(1976—), female, master, lixinxiu410@163.com.
Last Update: 2004-03-20