Computation of the eigenvalues of Fredholm–Stieltjes integral equations

Abstract

The Rayleigh–Ritz and the inverse iteration methods are used in order to compute the eigenvalues of Fredholm–Stieltjes integral equations, i.e. Fredholm equations with respect to suitable Stieltjes-type measures. Some applications to the so-called ‘charged’ (in German ‘belastete’) integral equation, and particularly the problem of computing the eigenvalues of a string charged by a finite number of cursors are given.

Keywords:

• Fredholm–Stieltjes integral equations
• Eigenvalues
• Rayleigh–Ritz method
• Inverse iteration method

Keywords:

• AMS Classifications: 45C05
• 45B05
• 65R20
• 26A42

Acknowledgments

This article was concluded in the framework of the Italian National Group for Scientific Computation (G.N.C.S.). The assistance of Dott. Rossano Rossi in numerical computations is gratefully recognized.