Sturm sequence recurrence formula for eigensolution of locally modified systems

Abstract

This paper proposes a recurrence formula for the fundamental equation derived on the basis of the Sturm sequence property for the eigensolution of locally modified systems. The fundamental equation expressed using a condensed matrix, of order equal of the mrder of the modified part of the system, requires the multiple calculation of a determinant. The number of calculations is equal to the order of the original system. The recurrence formula set forth in this paper avoids multiple evaluations of the determinant. Instead, a particular determinant evaluation is implemented by multiplying the previous determinant by a scalar. The effectiveness of the recurrence formula is confirmed using several numerical examples.