Efficient algorithms for eigenspace decompositions of Toeplitz matrices

This dissertation is devoted to the study of eigenvalue problems for Hermitian and real symmetric Toeplitz matrices. Spectral properties of these matrices are reviewed and some new results are derived. Algorithms for computing the eigenspaces of these matrices are studied. Some of the algorithms are generalized or extended, and their importance is emphasized. A new algorithm for computing all the eigenpairs of a real symmetric Toeplitz matrix is proposed. All the algorithms are implemented and tested through both MATLAB and FORTRAN77 codes.;The main focus of the dissertation is the algorithm for the eigenvalue problem of a real symmetric Toeplitz matrix. For matrices having well separated eigenvalues or eigenvalues of multiplicity at most 2, the method performs well and computes all the eigenpairs in ;The research reported in the dissertation will be of interest to people across many disciplines which include applied and computational mathematics, statistics, and signal processing.