ANZIAM J. 46(E) ppC1--C14, 2005.

Asymptotic correction and inverse eigenvalue problems: an overview

Alan L. Andrew
(Received 20 October 2004, revised 27 January 2005)

Abstract

Asymptotic correction was first used by Paine, de Hoog and Anderssen to improve the accuracy of finite difference approximations of higher Sturm--Liouville eigenvalues. Later it was used to develop an important class of methods for numerical solution of inverse Sturm--Liouville problems. It also shows promise as a method for the solution of more general inverse eigenvalue problems, including some involving partial differential equations and higher order operators. We critically review the literature on this subject and discuss some important open questions.

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Authors

Alan L. Andrew
Mathematics Department, La Trobe University, Victoria 3086, Australia. mailto:a.andrew@latrobe.edu.au

Published 7 March 2005, amended March 22, 2005. ISSN 1446-8735

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Copyright Austral. Mathematical Soc.; prepared March 22, 2005, from Andr.tex with anziamje.sty (v2.3a)