Twenty Years of Asymptotic Correction for Eigenvalue Computation
by
Alan L. Andrew
La Trobe University

A major defect of many classical methods of computing eigenvalues of differential operators is their poor performance for higher eigenvalues. The 1979 ANU thesis of John Paine [2] showed that, in certain circumstances, this defect could be largely overcome by a simple asymptotic correction technique. That thesis inspired much subsequent work. Results up to 1992 were surveyed in [1], which also noted a number of open questions. This paper assesses more recent work on the subject, with emphasis on the current status of the open questions mentioned in [1]. Results are also given of some numerical tests of a recent conjecture of the author concerning the use of asymptotic correction for Numerov approximations to eigenvalues of problems with natural boundary conditions. The results support the conjecture.

References

[1] A. L. Andrew ``Asymptotic correction of computed eigenvalues of differential equations'', Ann. Numer. Math. 1 (1994) 41-51.

[2] J. W. Paine ``Numerical approximation of Sturm-Liouville eigenvalues'', PhD thesis, Australian National University, 1979.

Date received: July 5, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-14.