NUMERICAL-CALCULATION OF THE EIGENVALUES AND EIGENVECTORS OF A SYMMETRIC SPARSE QUINDIAGONAL MATRIX

A recursive algorithm for the implicit derivation of the determinant of a symmetric sparse quindiagonal matrix derived from the finite difference discretisation of a self adjoint elliptic partial differential equation in a two-dimensional rectangular domain is developed in terms of its leading principal minors. The algorithm is shown to yield a sequence of polynomials from which the eigenvalues can be obtained by use of the well-known bisection process. Modifications to the inverse iteration method to allow for sparsity of the matrix arrays yields the required eigenvectors. © 1979, Taylor & Francis Group, LLC. All rights reserved.