Descent iterations for improving approximate eigenpairs of polynomial eigenvalue problems with general complex matrices
The paper is devoted to the study of two descent iterative methods, the generalized damped Newton method and the generalized damped Gauss-Newton method, both based on line search and designed to improve an approximate eigenvalue and the corresponding approximate eigenvector of polynomial eigenvalue problems with general complex matrices. To this end, it is supposed that an approximate eigenpair, obtained by a certain method, is available. Convergence theorems, without rate of convergence results, as well as numerical examples, are given. Finally, some empirical rate of convergence results are also mentioned.
scientific article; zbMATH DE number 1798912