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Class for Large-Scale Unconstrained Minimization

The class used in the BzzMath library for large-scale unconstrained minimization is [Pg.180]

The objects in the Bz zMinimizationLargeSparseNewton class exploit two iterative loops external and internal. The external loop is always the same, whereas the internal loop depends on the solution of the system (4.19) and on the calculation of the product Gp. [Pg.181]

1) If the structure of the Hessian matrix is not provided, the product Gp is performed using the approximation (4.18). In this case, the diagonal of the Hessian is used as preconditioner. [Pg.181]

2) If the structure of the Hessian is provided, it is exploited to calculate the same Hessian. In this case, the product Gp is performed by using the Hessian. Moreover, the first time that the Hessian is calculated, the rows and columns are sorted using the Reverse CuthiU-McKee Ordering method to make the selection of the preconditioner M easier. It is selected according to the number of coefficients within a band so as to use an object from the BzzFactor-izedSymmetricBand class. [Pg.181]

In the initial phase, a limited number of iterations for the internal loop is carried out in both the cases to obtain an estimation of Newton s prevision d. The number of iterations of the internal loop is progressively increased. [Pg.181]


See other pages where Class for Large-Scale Unconstrained Minimization is mentioned: [Pg.180]    [Pg.183]   


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