Title: Numerical solution of the eigenvalue problem for efficiently structured Hermitian matrices
Abstract: An iterative procedure is proposed for computing the eigenvalues and eigenvectors of a class of specially structured Hermitian Toeplitz matrices which includes Hermitian Toeplitz and Toeplitz-plus-Hankel matrices. The computational cost per eigenvalue-eigenvector for a matrix of order n is O(n2) in serial mode. Results of numerical experiments on Kac-Murdock-Szegö matrices and randomly generated real symmetric Toeplitz matrices and Toeplitz-plus-Hankel matrices of orders as high as 2000 are included.