On Remotest set and Random controls in Kaczmarz algorithm

Popa, Constantin

doi:10.2478/auom-2018-0015

Abstract

In this paper we analyse the Kaczmarz projection algorithm with Remotest set and Random control of projection indices and provide a suficient condition such that each projection index appears infinitely many times during the iterations.

References

[1] Ansorge R., Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equa- tions, Computing, 33 (1984), 367-375.10.1007/BF02242280
Search in Google Scholar Back to article
[2] Bauschke H.H., Borwein J.M., Legendre functions and the method of ran- dom Bregman projections, J. Convex Anal., 4(1997), 27-67.
Search in Google Scholar Back to article
[3] Censor, Y., Row-action methods for huge and sparse systems and their applications, SIAM Review, 23 (1981), 444-466.10.1137/1023097
Open DOI Search in Google Scholar Back to article
[4] Censor, Y., Zenios, S., Parallel Optimization: Theory, Algorithms and Applications, Oxford Univ. Press (1997)
Search in Google Scholar Back to article
[5] Censor, Y. Chen, W., Pajoohesh, H., Finite convergence of a subgradi- ent projections method with expanding controls, Appl. Math. Optim., 64 (2011), 273–285.10.1007/s00245-011-9139-8
Search in Google Scholar Back to article
[6] Combettes P., Hilbertian convex feasibility problem: Convergence of pro- jection methods, Appl. Math. Optim., 35 (1997), 311–330.10.1007/BF02683333
Search in Google Scholar Back to article
[7] Lorenz, D.A. et al., The linearized Bregman Method via Split Feasibil- ity Problems: Analysis and Generalizations, SIAM J. Imaging Sciences, 7(2)(2014), 1237-1262.10.1137/130936269
Search in Google Scholar Back to article
[8] Popa C. - Projection algorithms - classical results and developments. Ap- plications to image reconstruction, Lambert Academic Publishing - AV Akademikerverlag GmbH & Co. KG, Saarbrücken, Germany, 2012
Search in Google Scholar Back to article
[9] Strohmer, T., Vershynin, R., A randomized Kaczmarz algorithm with ex- ponential convergence, J. Fourier Anal. Appl. 15(2009), 262 - 278.10.1007/s00041-008-9030-4
Open DOI Search in Google Scholar Back to article
[10] Zouzias A., Freris N., Randomized Extended Kaczmarz for Solving Least Squares, SIAM Journal on Matrix Analysis and Applications, 34(2)92013), 773-793.10.1137/120889897
Search in Google Scholar Back to article

On Remotest set and Random controls in Kaczmarz algorithm

Abstract

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