The inverse Sturm-Liouville problem and the Rayleigh-Ritz method

Author:
Ole H. Hald

Journal:
Math. Comp. **32** (1978), 687-705

MSC:
Primary 65L15

DOI:
https://doi.org/10.1090/S0025-5718-1978-0501963-2

MathSciNet review:
0501963

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Abstract: In this paper we present an algorithm for solving the inverse Sturm-Liouville problem with symmetric potential and Dirichlet boundary conditions. The algorithm is based on the Rayleigh-Ritz method for calculating the eigenvalues of a two point boundary value problem, and reduces the inverse problem for the differential equation to a nonstandard discrete inverse eigenvalue problem. It is proved that the solution of the discrete problem converges to the solution of the continuous problem. Finally, we establish the stability of the method and give numerical examples.

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0501963-2

Article copyright:
© Copyright 1978
American Mathematical Society