Norms of Toeplitz Matrices with Fisher-Hartwig Symbols

Albrecht Boettcher, Jani Virtanen

Published 2006-06-01, updated 2006-12-18Version 2

We describe the asymptotics of the spectral norm of finite Toeplitz matrices generated by functions with Fisher-Hartwig singularities as the matrix dimension goes to infinity. In the case of positive generating functions, our result provides the asymptotics of the largest eigenvalue, which is of interest in time series with long-range memory.