Computation of eigenvalues and eigenvectors of a symmetric quindiagonal matrix

摘要

A recursive algorithm for the implicit derivation of the determinant of a symmetric quindiagonal matrix is developed in terms of its leading principal minors. The algorithm is shown to yield a Sturmian sequence of polynomials from which the eigenvalues can be obtained by use of the bisection process. Further modifications to the inverse iteration method using Wilkinson's technique (1962) yields the required eigenvectors.