Multilevel Toeplitz matrices and approximation by matrix algebras
Stefano Serra‐Capizzano, Eugene E. Tyrtyshnikov · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
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.