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I have an equation which has some unknown weights attached to various parameters. None of the weights are known. However, I have a history of data available with me which can be used to predict the unknown weights (at least approximately), may be after some trial and error and then one can use various optimization measures to improve upon the unknown weights. Is there any particular mathematical approach or software that can help to predict the weights in the least amount of time? (The number of data points is huge so that solving the equations for the unknown weights is not possible as the weights, which are the solutions of the equations, might be different for different sets of data points. So, getting an approximate estimate of the weights is the only choice)

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You are referring to multidimensional minimization. You are minimizing the error of a model depending on your weights (parameters). The error is usually the sum of the squares of the differences between the model prediction and the actual data. There are whole books on the subject, and introduction is in any numerical analysis text. I haven't read many, but like Numerical Recipes. Obsolete versions are free online.

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