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A NOTE ON THE BACKWARD ERRORS FOR INVERSE EIGENVALUE PROBLEMS

A NOTE ON THE BACKWARD ERRORS FOR INVERSE EIGENVALUE PROBLEMS
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摘要 In this note, we consider the backward errors for more general inverse eigenvalue problems by extending Sun's approach. The optimal backward errors are defined for diagonal-ization matrix inverse eigenvalue problem with respect to an approximate solution, and the upper and lower bounds are derived for the optimal backward errors. The results may be useful for testing the stability of practical algorithms. In this note, we consider the backward errors for more general inverse eigenvalue problems by extending Sun's approach. The optimal backward errors are defined for diagonal-ization matrix inverse eigenvalue problem with respect to an approximate solution, and the upper and lower bounds are derived for the optimal backward errors. The results may be useful for testing the stability of practical algorithms.
作者 Xinguo Liu Zhengjian Bai (Department of Mathematics, Ocean University of China, Qingdao 266071)
出处 《Journal of Computational Mathematics》 SCIE CSCD 2003年第2期201-206,共6页 计算数学（英文）
基金 This work was supported by NNSF of China.
关键词 Inverse eigenvalue problem Optimal backward error Upper bound Lower bound Inverse eigenvalue problem Optimal backward error Upper bound Lower bound
分类号 O241 [理学—计算数学]
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参考文献7

  • 1J. G. Sun, On the variation of the spectrum of a normal matrix, Lin. Alg. Appl., 246(1996),215-223.
  • 2J. G. Sun, Backward errors for the inverse eigenvalue problems, Numer. Math., 82(1999), 339-349.
  • 3Shu-Fang Xu, An Introduction to inverse algebraic eigenvalue problems, Peking University Press,1998.
  • 4S. Q. Zhou, H. Dai, The algebraic inverse eigenvalue problems (in Chinese), Henan Science and Technology Press, Zhengzhou, China, 1991.
  • 5J. G. Sun, The Perturbation Analysis of Matrix (in Chinese), Academic Press, China, 1987.
  • 6J. G. Sun and Q. Ye, The unsolvability of inverse algebraic eigenvalue problems almost everywhere,J. Comp. Math., 4(1986), 21-226.
  • 7S. F. Xu, The solvability of algebraic inverse eigenvalue problems almost everywhere, J. Comp.Math., Supplementary Issue, 1992, 152-157.
Journal of Computational Mathematics
2003年 第2期

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