Regularized Iterative Method for Ill-posed Linear Systems Based on\n Matrix Splitting

2020/04/14 by Ashish Kumar Nandi, Nandi, Ashish Kumar, Jajati Keshari Sahoo +1
Computer Science · Mathematics · Medicine · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Ultrasound Imaging and Elastography

paper · pdf · doi:10.48550/arxiv.2004.06388

openalex publication_date 2020/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the concept of matrix splitting is introduced to solve a large\nsparse ill-posed linear system via Tikhonov's regularization. In the\nregularization process, we convert the ill-posed system to a well-posed system.\nThe convergence of such a well-posed system is discussed by using different\ntypes of matrix splittings. Comparison analysis of both systems are studied by\noperating certain types of weak splittings. Further, we have extended the\ndouble splitting of [Song J and Song Y, Calcolo 48(3), 245-260, 2011] to double\nweak splitting of type II for nonsingular symmetric matrices. In addition to\nthat, some more comparison results are presented with the help of such weak\ndouble splittings of type I and type II.\n

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