Stable eigensolution of locally modified systems based on the Sturm sequence property

Abstract

This paper proposes an analytical procedure for the eigensolution of locally modified systems on the basis of the Sturm sequence property. The fundamental equation is derived retaining the advantages of the Sturm sequence property and is represented in a compact matrix form of the order of the number of modifications. This approach is useful for a modified system with many degrees of freedom, for which relatively few degrees of freedom are involved in the modifications. The accuracy and stability of this method are confirmed using several numerical examples with comparisons to the Householder bisection method.