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I would like to understand better how to solve least squares in a sequential/recursive way.

How to use weights in the least squares if the following problem:

y = A*a + B*b

where the estimation of a should be recursively updated, and b should be estimated each time separately.

Any recommendation for a book that can explain it well?

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The lecture notes found at Recursive Least Squares Estimation provide a nice explanation of the algorithm, plenty to use for programming your own solution. You might also take a look at the recursive shrinkage or boosting regression methods described in the free Hastie, Tibshirani and Friedman book Elements of Statistical Learning.

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  • $\begingroup$ What if we only have new measurements and not new parameters / bigger model? I think it is called Sequential Least Squares. $\endgroup$ – Royi Jul 30 '15 at 18:19

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