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Semiconvergence analysis of the randomized row iterative method and its extended variants
Author(s) -
Wu Nianci,
Xiang Hua
Publication year - 2021
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2334
Subject(s) - overdetermined system , underdetermined system , mathematics , iterative method , convergence (economics) , linear system , noise (video) , mathematical optimization , least squares function approximation , algorithm , simplicity , scale (ratio) , computer science , statistics , mathematical analysis , artificial intelligence , philosophy , epistemology , physics , quantum mechanics , estimator , economics , image (mathematics) , economic growth
Summary The row iterative method is popular in solving the large‐scale ill‐posed problems due to its simplicity and efficiency. In this work we consider the randomized row iterative (RRI) method to tackle this issue. First, we present the semiconvergence analysis of RRI method for the overdetermined and inconsistent system, and derive upper bounds for the noise error propagation in the iteration vectors. To achieve a least squares solution, we then propose an extended version of the RRI (ERRI) method, which in fact can converge in expectation to the solution of the overdetermined or underdetermined, consistent or inconsistent systems. Finally, some numerical examples are given to demonstrate the convergence behaviors of the RRI and ERRI methods for these types of linear system.