An eigenvalue recursion for Hermitian Toeplitz matrices
S.D. Morgera, Fazal Noor · 2003
A recursive algorithm is developed for finding the eigenvalues of a Hermitian Toeplitz matrix order n. The algorithm presented represents a generalization to the Hermitian case of one proposed by D.M. Wilkes and M.H. Hayes (1987) for the symmetric Toeplitz case. The method proposed uses Levinson's algorithm, or the more computationally efficient Hermitian Levinson algorithm of S.D. Morgera and H. Krishna (1987), at step k to form the characteristic equation of the next-larger principal submatrix of order k+1. The eigenvalues are then determined from the characteristic equation. The important issue of eigenvalue accuracy, which also applies to the Wilkes-Hayes procedure, is addressed.>