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Advances in Nonlinear Parameter Optimization - download pdf or read online

By R. Schmidt

ISBN-10: 3540113967

ISBN-13: 9783540113966

ISBN-10: 3540390804

ISBN-13: 9783540390800

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Extra resources for Advances in Nonlinear Parameter Optimization

Example text

The principal components of this selection procedure are shown in the logic diagram 7. At the beginning of the selection procedure i t is checked whether a vector ~ is equal to the null vector respectively whether its absolute value is less than an upper bound n. In this case i t is linearly dependent so that i t does not participate in the selection procedure. Remembering the selection procedure as described above we remark that the selection of the vectors for the building up of the m a t r i x ~ depends on the random sequence of the vectors d~.

2/16), when paying attention to numerical problems. If ~k is not great enough i t w i l l be necessary to return to Marquardt's method and that means to increase ~k adequately. The problem of assigning a rank to the matrix l~ also results from another reason which is connected with the sensitivity of the components of the direction vector r ~ I L due to disturbances in the system of linear equations from which the direction vector r k is obtained for the different minimizing methods. 5. For these and the above=mentioned reasons we have to derive five requirements for an always applicable method for the solution of nonlinear least squares problems.

Depending on these requirements we can develop a strategy for the selection of the next vector. e speak of a selection according to the criterion "maximal change of the slope". In order to apply the selection procedure on the basis of this criterion without great numerical effort i t is necessary to derive a relation between II~(xk)~k II 2 --ul+i and ll~(x3)~kll 2. 3/18). 1/9) --- we obtain after a short calculation ~k The notation,. _VIQ(xk ) _ in eq. °f the gradient vector vQ(x~). We see that i t is possible to calculate the value of A~ for each vec- 56 t o r ~ + l to be examined practically without any supplementary effort because the scalar a~ and the vector u_~ have to be determined for the calculation of the matrix ((~+I)T_D~+I)'1 anyhow.

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Advances in Nonlinear Parameter Optimization by R. Schmidt


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