An iterative method for solving general restricted linear equations
Shwetabh Srivastava and
Dharmendra K. Gupta
Applied Mathematics and Computation, 2015, vol. 262, issue C, 344-353
Abstract:
The Newton iterative method for computing outer inverses with prescribed range and null space is used in the non-stationary Richardson iterative method to develop an iterative method for solving general restricted linear equations. Starting with any suitably chosen initial iterate, our method generates a sequence of iterates converging to the solution. The necessary and sufficient conditions for the convergence along with the error bounds are established. The applications of the iterative method for solving some special linear equations are also discussed. A number of numerical examples are worked out. They include singular square, rectangular, randomly generated rank deficient matrices, full rank matrices and a set of singular matrices given in Matrix Computation Toolbox (mctoolbox) with the condition numbers ranging from order 1016 to 1050. The mean CPU time (MCT) and the error bounds are the performance measures used. Our results when compared with the results obtained by Chen (1997) leads to substantial improvement in terms of both computational speed and accuracy.
Keywords: Generalized inverse; Restricted linear system; Convergence analysis; Cramer rule; Subproper splitting; Characterization (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315005056
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:262:y:2015:i:c:p:344-353
DOI: 10.1016/j.amc.2015.04.047
Access Statistics for this article
Applied Mathematics and Computation is currently edited by Theodore Simos
More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().