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Perturbation analysis for the generalized eigenvalue and the generalized singular value problem

Section C Generalized Singular Values And Data Analysis

Part of the Lecture Notes in Mathematics book series (LNM,volume 973)

Abstract

The author has obtained some results in his recent work, which generalize some classical perturbation theorems for the standard eigenvalue problem Ax=λx to regular matrix pencils, and give a positive answer for an open question proposed by G. W. Stewart. A perturbation analysis for the generalized singular value decomposition suggested by Van Loan, C. C. Paige and M. A. Saunders has also been carried out.

Keywords

  • Perturbation Analysis
  • Generalize Eigenvalue Problem
  • Grassmann Manifold
  • Perturbation Bound
  • Matrix Pair

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported by the Alexander von Humboldt Foundation in Federal Republic of Germany.

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© 1983 Springer-Verlag

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Sun, Jg. (1983). Perturbation analysis for the generalized eigenvalue and the generalized singular value problem. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils. Lecture Notes in Mathematics, vol 973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062105

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  • DOI: https://doi.org/10.1007/BFb0062105

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