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On the convergence of nonstationary column‐oriented version of algebraic iterative methods
Author(s) -
Karimpour Mehdi,
Nikazad Touraj
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6358
Subject(s) - mathematics , flagging , convergence (economics) , column (typography) , relaxation (psychology) , iterative method , block (permutation group theory) , algorithm , mathematical optimization , matrix (chemical analysis) , local convergence , combinatorics , geometry , connection (principal bundle) , economics , economic growth , psychology , social psychology , materials science , archaeology , composite material , history
Recently, Elfving, Hansen, and Nikazad introduced a successful nonstationary block‐column iterative method for solving linear system of equations based on flagging idea (called BCI‐F). Their numerical tests show that the column‐action method provides a basis for saving computational work using flagging technique in BCI algorithm. However, they did not present a general convergence analysis. In this paper, we give a convergence analysis of BCI‐F. Furthermore, we consider a fully flexible version of block‐column iterative method (FBCI), in which the relaxation parameters and weight matrices can be updated in each iteration and the column partitioning of coefficient matrix is allowed to update in each cycle. We also provide the convergence analysis of algorithm FBCI under mild conditions.