Two-stage iterations based on composite splittings for rectangular linear systems |
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Authors: | Nachiketa Mishra Debasisha Mishra |
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Affiliation: | 1. Department of Mathematics, International Center for Theoretical Sciences (ICTS), TIFR, Bangalore 560089, India;2. Department of Computational and Data Sciences, Indian Institute of Science, Bangalore 560012, India;3. Department of Mathematics, National Institute of Technology Raipur, Raipur 492010, India |
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Abstract: | In this paper, we introduce a two-stage method to solve rectangular linear systems that exhibits faster convergence than typical stationary iterative methods. Under suitable conditions, we prove convergence of the new method. The number of outer iterations can be reduced by using a few significant number of inner iterations for efficient computations. Further, we perform a comparison analysis, and establish that a higher number of inner iterations ensures a smaller spectral radius of the global iteration matrix. We also discuss the uniqueness of a proper splitting, and illustrate different comparison theorems for different subclasses of proper splittings. |
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Keywords: | Moore–Penrose inverse Proper splitting Two-stage iteration Composite splitting Convergence theorem |
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