Unifying relations between iterative linear equation solvers and explicit Euler approximations for associated parabolic regularized equations

  • Iterative methods to solve linear equation systems are widely used in computational physics, engineering and many areas of applied mathematics. In recent works, performance improvements have been achieved based on modifications of several classes of iterative algorithms by various research communities driven by different perspectives and applications. This note presents a brief analysis of conventional and unifying perspectives by highlighting relations between several well-known iterative methods to solve linear equation systems and explicit Euler approximations of the associated parabolic regularized equations. Special cases of equivalence and general relations between different iterative methods such as Jacobi iterations, Richardson iterations, Steepest Descent and Quasi-Newton methods are shown and discussed. The results and discussion extend the conventional perspectives on these iterative methods and give way to intuitive physical interpretations and analogies. The accessibly presented relations give complementary educational insights and aim to inspire transdisciplinary developments of new iterative methods, solvers and preconditioners.

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Author:R. Sala, A. Schlüter, C. Sator, R. Müller
Parent Title (English):Results in Applied Mathematics
Document Type:Article
Language of publication:English
Publication Date:2022/07/21
Year of Publication:2021
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2022/07/21
Tag:Iterative methods; Parabolic regularization; Preconditioners; Sparse linear equations
GND-Keyword:Iterative methods; Sparse linear equations; Preconditioners; Parabolic regularization
Issue:Volume 13, February 2022, 100227
Number of page:6
Faculties / Organisational entities:Kaiserslautern - Fachbereich Maschinenbau und Verfahrenstechnik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Zweitveröffentlichung