Download PDF by R. Schmidt: Advances in Nonlinear Parameter Optimization

By R. Schmidt

ISBN-10: 3540113967

ISBN-13: 9783540113966

ISBN-10: 3540390804

ISBN-13: 9783540390800

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For these reasons selected test problems only come into question to judge the different minimizing methods. Among others, Bard [15], McKeown [16], and Box [17] have made comparing investigations of minimizing methods for the solution of nonlinear least squares problems. x~! I t I Co~colote ~_" '1 J-~Q(-~h:-2(-~k)T,-P-~(-~k) I,, Finish the I iteration J without J result ! Finish thel iteration ! (~k,~........... 1 = X k + OL,min,_r,k [.. . . [ I Logic diagram 4: Principal components of Meyer's method for the solution of nonlinear ]east squares prob]emso 27 Here we present a summary of the results which have been obtained by partly very extensive investigations.

With these considerations we finish the survey of well-known special minimizing methods for the solution of nonlinear least squares problems. I t is to remark that this survey is certainly not complete (for some further methods see for instance [1]). ~ ........................ In the two preceding sections we have shown some possibilities how to solve nonlinear least squares problems with the help of universal and special minimizing methods. There is the obvious question which kind of method w i l l be "better" suited for the solution of these problems.

Moreover he has no possibility to determine the computation time exactly to a certain extent. An error of ~ 25 % in the computation time cannot be ruled out. Therefore the only reliable criterion is the number of function evaluations. Applying this criterion i t turns out that the special minimizing methods are superior to the universal minimizing methods although the difference is not so striking as in the case of the test problems investigated by Bard. Among other things this is a consequence of the different test problems under consideration and of the different applied c r i t e r i a .

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Advances in Nonlinear Parameter Optimization by R. Schmidt


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