A perturbation result for generalized eigenvalue problems and its application to error estimation in a quadrature method for computing zeros of analytic functions

Kravanja, Peter; Sakurai, Tetsuya; Sugiura, Hiroshi; Van Barel, Marc

doi:10.1016/J.CAM.2003.03.003

Title

A perturbation result for generalized eigenvalue problems and its application to error estimation in a quadrature method for computing zeros of analytic functions

Author

Kravanja, Peter

Sakurai, Tetsuya

Sugiura, Hiroshi

Van Barel, Marc

Abstract

We consider the quadrature method developed by Kravanja et al. (BIT 39 (4) (1999) 646) for computing all the zeros of an analytic function that lie inside the unit circle. A newperturbation result for generalized eigenvalue problems allows us to obtain a detailed upper bound for the error between the zeros and their approximations. To the best of our knowledge, it is the 9rst time that such an error estimate is presented for any quadrature method for computing zeros of analytic functions. Numerical experiments illustrate our results.

Language

English

Source (journal)

Journal of computational and applied mathematics. - Antwerp, 1975, currens

Publication

Antwerp : 2003

ISSN

0377-0427 [print]

1879-1778 [online]

DOI

10.1016/J.CAM.2003.03.003

Volume/pages