How to prove that a preconditioner cannot be superlinear |
| |
Authors: | S Serra Capizzano E Tyrtyshnikov |
| |
Affiliation: | Dipartimento di Chimica, Fisica e Matematica, Università dell'Insubria - Sede di Como, Via Valleggio 11, 22100 Como, Italy ; Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina 8, Moscow 117333, Russia |
| |
Abstract: | In the general case of multilevel Toeplitz matrices, we recently proved that any multilevel circulant preconditioner is not superlinear (a cluster it may provide cannot be proper). The proof was based on the concept of quasi-equimodular matrices, although this concept does not apply, for example, to the sine-transform matrices. In this paper, with a new concept of partially equimodular matrices, we cover all trigonometric matrix algebras widely used in the literature. We propose a technique for proving the non-superlinearity of certain frequently used preconditioners for some representative sample multilevel matrices. At the same time, we show that these preconditioners are, in a certain sense, the best among the sublinear preconditioners (with only a general cluster) for multilevel Toeplitz matrices. |
| |
Keywords: | |
|
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 |
|
点击此处可从《Mathematics of Computation》下载全文 |
|