<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Recent developments in the field of image reconstruction have given rise to the use of projective iterative methods, such as Kaczmarz and Jacobi, when solving inconsistent linear least squares problems. In this paper we try to generalize previous results concerning extended block versions of these two algorithms. We replace the inverse operator with the Moore-Penrose pseudoinverse and try to prove convergence under weaker assumptions. In order to accomplish this task, we show that these algorithms are special cases of a general iterative process for which convergence is already established. </p></abstract>

Recent developments in the field of image reconstruction have given rise to the use of projective iterative methods, such as Kaczmarz and Jacobi, when solving inconsistent linear least squares problems. In this paper we try to generalize previous results concerning extended block versions of these two algorithms. We replace the inverse operator with the Moore-Penrose pseudoinverse and try to prove convergence under weaker assumptions. In order to accomplish this task, we show that these algorithms are special cases of a general iterative process for which convergence is already established.

Weaker assumptions for convergence of extended block Kaczmarz and Jacobi projection algorithms

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Recent developments in the field of image reconstruction have given rise to the use of projective iterative methods, such as Kaczmarz and Jacobi, when solving...

Weaker assumptions for convergence of extended block Kaczmarz and Jacobi projection algorithms

Published Online: Sep 21, 2017

Page range: 49 - 60

Received: Nov 15, 2015

Accepted: Apr 30, 2016

DOI: https://doi.org/10.1515/auom-2017-0004

Keywords
Inconsistent linear least squares problem, extended block Kaczmarz algorithm, extended block Jacobi with relaxation parameters algorithm, Moore-Penrose pseudoinverse, clustering

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Weaker assumptions for convergence of extended block Kaczmarz and Jacobi projection algorithms

Published Online: Sep 21, 2017

Page range: 49 - 60

Received: Nov 15, 2015

Accepted: Apr 30, 2016

DOI: https://doi.org/10.1515/auom-2017-0004

KeywordsInconsistent linear least squares problem, extended block Kaczmarz algorithm, extended block Jacobi with relaxation parameters algorithm, Moore-Penrose pseudoinverse, clustering

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Inconsistent linear least squares problem, extended block Kaczmarz algorithm, extended block Jacobi with relaxation parameters algorithm, Moore-Penrose pseudoinverse, clustering