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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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 |
|---|---|
| Publication: | Simulation |
| Publisher: | Society for Computer Simulation International |
| 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.ac.in/id/eprint/13067 |
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