Stable eigensolution of locally modified systems based on the Sturm sequence property (Q1190408)

An analytical procedure for the problem cited in the title is proposed. The fundamental equation is expressed in terms of condensed matrices with the order of the modified part; this equation is of the same type as the one obtained, in a problem of solid mechanics, by the second author, \textit{T. Yoshimura} and \textit{K. Takamura} [Internat. J. Numer. Methods Engin. 6, 441-442 (1973; MR 48.5478)]. The procedure supposes that all the eigenvalues and eigenvectors of the original system are known. Simple examples verify the accuracy of the method if relatively few degrees of freedom are involved in the modifications.