Abstract
Recently the method of Kaczmarz 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 Cimmino converges (almost) always but shows some disadvantages. A modification of the Cimmino-method is presented which makes it as interesting as the Kaczmarzmethod. In certain cases, the new method is even faster.
Zusammenfassung
In jüngster Zeit erfuhr, das Verfahren von Kaczmarz zur Lösung linearer Gleichungssysteme wieder ein stärkeres Interesse. Es konvergiert stets gegen eine Lösung, sofern wenigstens eine Lösung existiert. Auch das Verfharen von Cimmino konvergiert (fast) immer, zeigt jedoch einige Nachteile. Eine Abänderung des Cimmino-Verfahrens wird vorgestellt, die es dem Kaczmarz-Verfahren in gewissem Umfange ebenbürtig macht. Gelegentlich ist es sogar schneller.
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Ansorge, R. Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equations. Computing 33, 367–375 (1984). https://doi.org/10.1007/BF02242280
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DOI: https://doi.org/10.1007/BF02242280