Multilevel Toeplitz matrices and approximation by matrix algebras

Stefano Serra-Capizzano; Eugene E. Tyrtyshnikov

doi:10.1117/12.325700

2 October 1998 Multilevel Toeplitz matrices and approximation by matrix algebras

Stefano Serra-Capizzano, Eugene E. Tyrtyshnikov

Proceedings Volume 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII; (1998) https://doi.org/10.1117/12.325700
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

Optimal preconditioners are of paramount importance for cg-like methods since they make them converge superlinearly. In preceding papers, we proved that any preconditioner belonging to partially equimodular spaces is not optimal for multilevel Toeplitz matrices where the aforementioned class of spaces includes all the known and used trigonometric matrix algebras. Here we survey and refine these results by focusing our attention on the more difficult case in which the multilevel Toeplitz matrices are Hermitian.

Citation Download Citation

Stefano Serra-Capizzano and Eugene E. Tyrtyshnikov "Multilevel Toeplitz matrices and approximation by matrix algebras", Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); https://doi.org/10.1117/12.325700

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