Sturm sequence analysis of a diagonally bordered matrix

Abstract

In this paper, the eigenvalues of a diagonally bordered or arrowhead matrix are obtained using a bisection process based on a Sturm sequence of polynomials derived from the determinantal form. Techniques for accelerating the process by Newton's method on scaled recursive sequences are also discussed.Similarly the eigenvectors are derived from an inverse iteration process based on an LU forward and back substitution solution strategy.

Keywords:

• Sturm sequence
• diagonally bordered matrix
• eigenvalues and eigenvectors

C.R Categories:

• G.1.3