Authors:	Sobania, Dominik Schmitt, Jonas Köstler, Harald Rothlauf, Franz
Title:	Genetic programming for iterative numerical methods
Online publication date:	3-Aug-2022
Year of first publication:	2022
Language:	english
Abstract:	We introduce GPLS (Genetic Programming for Linear Systems) as a GP system that finds mathematical expressions defining an iteration matrix. Stationary iterative methods use this iteration matrix to solve a system of linear equations numerically. GPLS aims at finding iteration matrices with a low spectral radius and a high sparsity, since these properties ensure a fast error reduction of the numerical solution method and enable the efficient implementation of the methods on parallel computer architectures. We study GPLS for various types of system matrices and find that it easily outperforms classical approaches like the Gauss–Seidel and Jacobi methods. GPLS not only finds iteration matrices for linear systems with a much lower spectral radius, but also iteration matrices for problems where classical approaches fail. Additionally, solutions found by GPLS for small problem instances show also good performance for larger instances of the same problem.
DDC:	004 Informatik 004 Data processing 330 Wirtschaft 330 Economics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 03 Rechts- und Wirtschaftswissenschaften
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-7483
Version:	Published version
Publication type:	Zeitschriftenaufsatz
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Journal:	Genetic programming and evolvable machines 23
Pages or article number:	253 278
Publisher:	Springer Science + Business Media B.V.
Publisher place:	Dordrecht u.a.
Issue date:	2022
ISSN:	1573-7632
Publisher DOI:	10.1007/s10710-021-09425-5
Appears in collections:	JGU-Publikationen