The numerical calculation of the eigenvalues and eigenvectors of a symmetric sparse quindiagonal matrix
David John Evans, C.C. Rick · International Journal of Computer Mathematics · 1979
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.