Eigenproblem solution by a combined Sturm sequence and inverse iteration technique

Abstract

Abstract This article presents an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = λBq with band symmetric A and B, B being also positive definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems including free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.