@inproceedings{a889c743df4243aca5f1e59105f1b4c2,
title = "Parallel combined chebyshev and least squares iterations in the krylov subspaces",
abstract = "The combined Chebyshev−Least Squares iterative processes in the Krylov subspaces to solve symmetric and non-symmetric systems of linear algebraic equations (SLAEs) are proposed. This approach is a generalization of the Anderson acceleration of the Jacobi iterative method as an efficient alternative to the Krylov methods. The algorithms proposed are based on constructing some basis of the Krylov subspaces and a minimization of the residual vector norm by means of the least squares procedure. The general process includes periodical restarts and can be considered to be an implicit implementation of the Krylov procedure which can be efficiently parallelized. A comparative analysis of the methods proposed and the classic Krylov approaches is presented. A parallel implementation of the iterative methods on multi-processor computer systems is discussed. The efficiency of the algorithms is demonstrated via the results of numerical experiments on a set of model SLAEs.",
keywords = "Anderson acceleration, Chebyshev iterative algorithms, Convergence of iterations, Krylov subspaces, Least squares, Numerical experiments, Numerical stability",
author = "Yana Gurieva and Valery Il{\textquoteright}in",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.; 14th International Scientific Conference on Parallel Computational Technologies, PCT 2020 ; Conference date: 27-05-2020 Through 29-05-2020",
year = "2020",
month = jan,
day = "1",
doi = "10.1007/978-3-030-55326-5_12",
language = "English",
isbn = "9783030553258",
series = "Communications in Computer and Information Science",
publisher = "Springer Gabler",
pages = "162--177",
editor = "Leonid Sokolinsky and Mikhail Zymbler",
booktitle = "Parallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers",
address = "Germany",
}