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.Full text not available from this repository.
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|
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