Iterative refinement of solution with biparameter for solving ill-conditioned systems of linear algebraic equations.
type: Item
instance of: scholarly article
title: Iterative refinement of solution with biparameter for solving ill-conditioned systems of linear algebraic equations.
zbMATH Open document ID: 1034.65025
DOI: 10.1016/S0096-3003(01)00141-2
author: Rong Shao
author: Guo-he Xue
author: Xinyuan Wu
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The authors describe an iterative refinement algorithm for the improvement of the computed solution of a positive definite, ill-conditioned system of linear equations. The algorithm uses two parameters that play the role of ``regularizing parameters'', as in the classical iterative Tikhonov regularization method. The authors prove convergence of the algorithm under some supplementary assumptions on the two parameters and describe numerical experiments and comparisons of their method with some Wilkinson's and Tikhonov's solvers.
Mathematics Subject Classification ID: 65F22
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1861165
zbMATH Keywords: iterative improvement
zbMATH Keywords: ill-conditioned linear systems
zbMATH Keywords: iterative refinement algorithm
zbMATH Keywords: Tikhonov regularization method
zbMATH Keywords: comparison of method
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
reviewed by: Constantin Popa
MaRDI profile type: Publication
cites work: Symmetric decomposition of a positive definite matrix
cites work: Iterative refinement of the solution of a positive definite system of equations
cites work: Q4871634
cites work: Q5674306
cites work: Numerical methods for solving linear least squares problems
cites work: Q3857636
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description: scientific article; zbMATH DE number 1861165