Sampling eigenvalues by Hermite revisited

ABSTRACT

We show how the Hermite sampling method can be used to approximate the eigenvalues of Sturm-Liouville problems. Because it involves the derivatives with respect to the eigenvalue parameter, it requires more smoothness on the coefficients and integrating a one parameter family of matrix Sturm-Liouville operators to generate the required samples.

KEYWORDS:

• Eigenvalues of Sturm Liouville
• Shannon sampling theorem
• computational spectral theory
• Hermite interpolation
• matrix Sturm Liouville

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34L16
• 94A20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author sincerely thanks King Fahd University of Petroleum and Minerals (KFUPM), for its hospitality and support during his visit in Fall 2017.