论文信息 - How Bad Can Positive Definite Toeplitz Matrices Be?

How Bad Can Positive Definite Toeplitz Matrices Be?

Let and suppose f does not vanish identically. Denote by Tn(f) the n×n Toeplitz matrix generated by f and let κ(Tn(f)) stand for the spectral condition number of Tn(f). Recently we proved that if f is not pathological, then for some constant γ>0. In this note we show that an approximation theorem by Yano easily implies the sharper estimate . We also characterize a class of functions f for which and we establish a conjecture concerning pathological functions f.

Stefano Serra Capizzano

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