Extension of Lanczos’ Method of Fundamental Eigenvalue Approximation

Abstract

A method introduced by Lanczos for the approximate determination of fundamental eigenvalues of one-dimensional continuous systems is extended to permit the determination of higher eigenvalues as well, and a modification is introduced which yields better accuracy for the same number of approximating equations. Illustrations are presented demonstrating applications of the method to systems with discontinuities and to the frequency determination in nonlinear oscillation problems.