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DATA SELECTION WITH HESSIAN MATRIX by HannaAriniParhusip1

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									Proceeding of IndoMS International Conference on Mathematics and Its Applications (IICMA) 2009, Oct 12-13
                                                               2009, ISBN:978-602-96426-0-5, 0341-0352.



                       DATA SELECTION WITH HESSIAN MATRIX

                                           H. A. Parhusip
                                                Abstract.
Procedures of data selection used for an optimization by a quadratic function of two variables
are shown here. The parameters can be obtained by the least square method and applying the
pseudo-inverse. After the parameters of the quadratic function are known, the eigenvalues of
its Hessian matrix must be computed. If the Hessian matrix is positive definite (shown by all
eigenvalues are positive) then a minimization problem can be
posed. If it is indefinite, then a minimization problem can not defined based on the given
data. Though the number of data is larger than the number of parameters, it is not guaranteed
that one may have always a feasible set. Therefore we handle this problem by introducing
constraints to the minimization problem to find the value of each parameter. The constraints
are obtained by forcing the Hessian matrix to be (semi)positive definite.
Finally we get any data can be in a feasible set. Thus the minimizer can be obtained though
only locally.
Key words and Phrases: Hessian, eigenvalues, least square

								
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