Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equations
type: Item
instance of: scholarly article
title: Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equations
zbMATH Open document ID: 0537.65027
DOI: 10.1007/BF02242280
author: Rainer Ansorge
published in: Computing
publication date: 1985-01-01T00:00:00Z
review text: Recently the method of \textit{S. Kaczmarz} [cf. Bull. Int. Acad. Polon. Sci., Ser. A 1937, 355-357 (1937; Zbl 0017.31703)] for the solution of linear equations became interesting again. This method converges always to a solution provided that at least one solution exists. Also the method of \textit{G. Cimmino} [cf. Ric. Sci. progr. tecn. econom. naz. 1, 326-333 (1938; Zbl 0018.41802)] converges (almost) always but shows some disadvantages. A modification of the Cimmino-method is presented which makes it as interesting as the Kaczmarz-method. In certain cases the new method is even faster.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 3854301
zbMATH Keywords: fast convergence
zbMATH Keywords: Cimmino-method
zbMATH Keywords: non-regular coefficient matrices
zbMATH Keywords: Kaczmarz-method
MaRDI profile type: Publication
cites work: Über die Konvergenz der Iterationsverfahren zur Auflösung linearer Gleichungssysteme im Falle einer singulären Koeffizientenmatrix
cites work: Q5783767
cites work: Q5768822
cites work: On the Solution of Singular and Semidefinite Linear Systems by Iteration
cites work: Q4109207
cites work: Projection method for solving a singular system of linear equations and its applications
cites work: Characterization of linear stationary iterative processes for solving a singular system of linear equations
full work available at URL: https://doi.org/10.1007/bf02242280
OpenAlex ID: W304534868
description: scientific article; zbMATH DE number 3854301