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A concise algorithm to solve over-/under-determined linear systems

Lord, Eric A and Sen, SK and Venkaiah, VCh (1990) A concise algorithm to solve over-/under-determined linear systems. In: Simulation, 54 (5). pp. 239-240.

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Abstract

An $ O(mn^2)$ direct algorithm to compute a solution of a system of m linear equations Ax=b with n variables is presented. It is concise and matrix inversion-free. It provides an in-built consistency check and also produces the rank of the matrix A. Further, if necessary, it can prune the redundant rows of A and convert A into a full row rank matrix thus preserving the complete information of the system. In addition, the algorithm produces the unique projection operator that projects the real (n)-dimensional space orthogonally onto the null space of A and that provides a means of computing a relative error bound for the solution vector as well as a nonnegative solution.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Society for Computer Simulation International
Keywords: linear equations;linear programming;Moore- Penrose inverse;nonnegative solution of linear equations;projection operator
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 19 Feb 2008
Last Modified: 25 Apr 2012 07:47
URI: http://eprints.iisc.ernet.in/id/eprint/13067

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