Publication at Faculty of Mathematics and Physics |
2016
Abstract
An asymptotic convergence analysis of a new multilevel method for numerical solution of eigenvalues and eigenvectors of symmetric and positive definite matrices is performed. The analyzed method is a generalization of the original method that has recently been proposed by R.
Kuel and P. Vanek (DOI: 10.1002/nla.1975) and uses a standard multigrid prolongator matrix enriched by one full column vector, which approximates the first eigenvector.
The new generalized eigensolver is designed to compute eigenvectors. Their asymptotic convergence in terms of the generalized residuals is proved, and its convergence factor is estimated.
The theoretical analysis is illustrated by numerical examples.