WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 14, 2015
The Least Norm Solution of the Linear System via a Quadratic Penalty Function
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Abstract: In this paper, the linear system of equations in unknowns is formulated as a quadratic programming problem, and the least norm solution for the consistent or inconsistent system of the linear equations is investigated using the optimality conditions of the quadratic penalty function (QPF). In addition, several algebraic characterizations of the equivalent cases of the QPFs are given using the orthogonal decompositions and the generalized inverses of the coefficient matrices obtained from optimality conditions. It is seen that the least norm solution of the consistent or inconsistent system of the linear equations can be found with the penalty method. In addition, it is shown that the method can be applied to all systems of the linear equations to find the least norm solution. Numerical examples are presented by using the analytic results that were obtained.
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Pages: 292-300
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 14, 2015, Art. #28