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*Subject*: maximizing sum of squares*From*: Craig Markwardt <craigmnet(at)astrog.physics.wisc.edu>*Date*: 25 Nov 1998 10:43:41 -0600*Newsgroups*: sci.math.num-analysis*Organization*: U. Wisc. Madison Physics -- Compact Objects*Reply-To*: craigmnet(at)astrog.physics.wisc.edu*Xref*: news.doit.wisc.edu sci.math.num-analysis:37490

Greetings-- There are lots of packages and advice on the network concerning the *minimization* of the sum of squares, since that is what is usually needed for nonlinear least squares curve fitting. I have a problem where I need to *maximize* the sum of squares. The application is to timing properties of astrophysical objects where one desires to find the best-fitting signal frequency which maximizes the amplitude. The statistic to be maximized is distributed like a chi-squared, but is strictly bounded at the upper end (ie, it doesn't diverge). For least squares problems, I typically use MINPACK-1, which works great. Obviously I would need to modify MINPACK to maximize instead of minimize. One naive way to do that would be to change the sign of the step taken at each iteration. Somehow I think it's more complicated than that, however. For example, MINPACK goes through lots of gyrations to find an appropriate Levenberg-Marquardt parameter, and its not evident to me that those calculations apply for my application. Can anybody suggest a clear way to modify the LM fitting technique for maximization instead of minimization? Thanks, Craig -- -------------------------------------------------------------------------- Craig B. Markwardt, Ph.D. EMAIL: craigmnet@astrog.physics.wisc.edu --------------------------------------------------------------------------

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