Abstract
The Lanczos algorithms can be used to find a symmetric tridiagonal matrix from its eigenvalues and the first components of its normalized eigenvectors. The direct application of this method to discretized Strum-Liouville problems is useless since the finite difference eigenvalues behave quite differently asymptotically than the eigenvalues of the continuous Strum-Liouville problem. We suggest a multiplicative asymptotic correction for the discrete equation. The corrected equations can still be solved, at least approximately, by an algorithm similar to the Lanczos algorithm. Numerical experiments show that this approach leads to results of modest accuracy.
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