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I have a set of measurements that I want to fit to a linear model with a bunch of parameters. I do this as [itex]\theta=(H^TH)^{-1}H^Tx[/itex], where θ are the parameters and x is the set of measurements. The problem is that I'd like to reduce the number of parameters in the fit. I'd like to chose the subset of N parameters that gives the best fit, such that no other combination of N parameters works better.

Is there any way I can determine what is the best subset of N parameters without having to try all of them? I have seen that with order recursive least squares I can add parameters sequentially to improve the fit, but this approach does not guarantee that the N parameters that I have selected are the best combination.

Thank you very much for any help,

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# Determine optimal vectors for least squares

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