# Solving least squares problems

@inproceedings{Lawson1995SolvingLS, title={Solving least squares problems}, author={Charles L. Lawson and Richard J. Hanson}, booktitle={Classics in applied mathematics}, year={1995} }

Since the lm function provides a lot of features it is rather complicated. So we are going to instead use the function lsfit as a model. It computes only the coefficient estimates and the residuals. Now would be a good time to read the help file for lsfit. Note that lsfit supports the fitting of multiple least squares models and weighted least squares. Our function will not, hence we can omit the arguments wt, weights and yname. Also, changing tolerances is a little advanced so we will trust…

## 4,349 Citations

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A powerful proximal gradient method is presented that can be used to find good, if not the best, hyper-parameters for least squares problems and is able to cut the test error of standard least squares in half.

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Two closely related methods for solving the least squares problem with equality constraints (LSE) are considered. The first is the direct elimination (DE) method that is implemented using Modified…

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Three order-recursive formulas for the Moore-Penrose pseudoinverses of matrices which are the improved and extended Greville formulas (1960) are presented, which are much easier to derive and clearer and simpler.