British Journal of Mathematics & Computer Science, ISSN: 2231-0851,Vol.: 21, Issue.: 1

Original-research-article

Large Matrices Inversion Using the Basis Exchange Algorithm

Leon Bobrowski^1,2*

Article Information
Editor(s):
(1) Sergio Serrano, Department of Applied Mathematics, University of Zaragoza, Spain.
(2) Metin Basarir, Department of Mathematics, Sakarya University, Turkey.
(3) Paul Bracken, Department of Mathematics, The University of Texas-Pan American, Edinburg, TX 78539, USA.
Reviewers:
(1) Marija Milojevic Jevric, Mathamatical Institute SANU, Serbia.
(2) Carlo De Gaetani, Politecnico di Milano, Italy.
(3) Nikolaos Ploskas, Carnegie Mellon University, Pittsburgh, PA, USA.
Complete Peer review History: http://www.sciencedomain.org/review-history/18203

Data exploration tasks often require inversion of large matrices. The paper presents a new method of matrices inversion, which uses the basis exchange algorithm controlled by the convex and piecewise linear (CPL) inversion criterion function. Using basis exchange algorithms might increase the dimension of the inverted matrices and computational efficiency of the inversion tasks. Basis exchange algorithms are based on the Gauss-Jordan transformation which is used e.g. in the famous Simplex algorithm applied in linear programming.

Keywords :

Data exploration; large matrices inversion; basis exchange algorithm; Gauss-Jordan transformation; convex and piecewise linear (CPL) criterion functions.

Full Article - PDF    Page 1-11

DOI : 10.9734/BJMCS/2017/31778