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

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.

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