A strategy utilising partial sturm sequences for determining the eigenvalues of a symmetric matrix

Abstract

A recursive algorithm for the implicit derivation of the determinant of a symmetric sparse quindiagonal matrix derived from the finite difference discretization of a self adjoint elliptic partial differential equation in a two dimensional rectangular domain is developed in terms of its leading principal minors (Evans & Rick, 1979). The algorithm is shown to yield a sequence of polynomials from which the eigenvalues can be obtained in ascending or descending order of magnitude by use of the well known Secant method. This method is then speeded up considerably by the use of Partial Sturm sequences, thus saving the time used in calculating the full sequence for every iteration. A similar strategy has been given previously in Evans et al. (1981)

Keywords:

• Partial Sturm sequence
• Secant method
• Gaussian elimination

C.R. Categories::

• G1.3
• G1.8