Numerical Algorithms

, Volume 69, Issue 1, pp 227–251 | Cite as

The inexact fixed matrix iteration for solving large linear inequalities in a least squares sense

  • Yuan Lei
Original Paper


A fixed matrix iteration algorithm was proposed by A. Dax (Numer. Algor. 50, 97–114 2009) for solving linear inequalities in a least squares sense. However, a great deal of computation for this algorithm is required, especially for large-scale problems, because a least squares subproblem should be solved accurately at each iteration. We present a modified method, the inexact fixed iteration method, which is a generalization of the fixed matrix iteration method. In this inexact iteration process, the classical LSQR method is implemented to determine an approximate solution of each least squares subproblem with less computational effort. The convergence of this algorithm is analyzed and several numerical examples are presented to illustrate the efficiency of the inexact fixed matrix iteration algorithm for solving large linear inequalities.


Linear inequalities Inconsistent systems Fixed matrix iteration Inexact fixed matrix iteration Krylov subspace LSQR method 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.College of Mathematics and EconometricsHunan UniversityChangshaPeople’s Republic of China

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