Semisectoriality condition numbers of large Toeplitz matrices, and one asymptotic problem
by
Sergey M. Grudsky
Rostov-on-Don State University (Russia)
Coauthors: Albrecht Böttcher (Technische Universität Chemnitz), Stanislav S. Mikhalkovich (Rostov-on-Don State University)

This report is devoted to asymptotic estimates for the condition numbers \kappa(T_n(a))=||T_n(a)|| ||T_n^-1(a)|| of large n×n Toeplitz matrices T_n(a) in the case where the symbol a is in L^\infty and Re a >= 0 almost everywhere. We describe several classes of symbols a for which \kappa(T_n(a)) increases like (logn)^\alpha, n^\alpha, or e^\alphan. Analogous estimates are obtained for Wiener-Hopf integral equations on finite intervals with large length L. On this basis one diffraction problem is considered.

Date received: May 16, 2000