Extreme eigenvalues of real symmetric Toeplitz matrices
Spectral equations (with possibly unknown singularities) are used for computing the smallest and largest eigenvalues of real symmetric Toeplitz matrices (other papers on this problem are quoted) from two equations, one for the even and one for the odd eigenvalues, that have already been used by others. The present paper presents a shorter analysis of the rootfinder used in two other works. This also leads to a better stopping rule, based on rational rather than on polynomial approximation. The paper also presents an error analysis not contained in those other works. Numerical results given concern positive semidefinite Toeplitz matrices earlier considered by G. Szegő, Cybenko, and others.
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