Three-step alternating and preconditioned scheme for rectangular matrices
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In this article, a three-step alternating iterative scheme for rectangular system has been proposed. The convergence and comparison analysis of the proposed method has been discussed for the class of semi-monotone matrices and which confirms the faster convergence of our scheme. A preconditioned approach is also presented in this paper to relax the semi-monotonicity condition. The preconditioned approach is very promising and converges faster than some of existing schemes. We finally validated all the theoretical results by some numerical examples.
KeywordsNonnegativity Moore–Penrose inverse Semi-monotone Proper splitting Convergence theorem Comparison theorem
Mathematics Subject Classification15A09 65F10 65F15 65F20
We would like to thank Dr. Chinmay Kumar Giri, Lecturer, Department of Mathematics, Govt. Women’s College Baripada, India for his helpful suggestions. The authors also thank the referee for his/her helpful comments and suggestions which led to a much improved presentation of the paper.
- 8.Climent, J.J., Devesa, A., Perea, C.: Convergence Results for Proper Splittings. Recent Advances in Applied and Theoretical Mathematics, pp. 39–44. World Scientific and Engineering Society Press, Singapore (2000)Google Scholar
- 24.Mishra, D.: Proper weak regular splitting and its application to convergence of alternating iterations. arXiv preprint arXiv:1602.01972 (2016)
- 35.Wang, G., Zhang, N.: Some results on parallel alternating methods. Int. J. Appl. Math. Comput. 3(1), 65–69 (2011)Google Scholar