On the eigenvalue problem for toeplitz matrices generated by rational functions
Willian F. Trench · Linear and Multilinear Algebra · 1985
Formulas are given for the characteristic polynomials {pn (λ)}and the eigenvectors of the family {Tn }of Toeplitz matrices generated by a formal Laurent series of rational function R(z). The formulas are in terms of the zeros of a certain fixed polynomial with coefficients which are simple functions of λ and the coefficients of R(z). The complexity of the formulas is independent ofn.