Let us assume we have a least squares fitting problem.

$${\bf v_o} = \min_{\bf v}\{\|{\bf \Phi v-d}\|_2^2\}$$

Where $${\bf \Phi} \in \mathbb R^{N\times k}\\{\bf d} \in \mathbb R^{N\times1}$$ Furthermore let's assume $N>>k$. In other words, many more data points than degrees of freedom to fit.

If we use C-G and want to solve the Normal equations : $${\bf v_o} = ({\bf \Phi}^T{\bf \Phi})^{-1}({\bf \Phi}^T{\bf d})$$ It would seem to me that it will be overkill to fit all $N$ points in every C-G iteration. Is there some way to estimate how few data points we can get away with fitting, and how to choose these. Maybe we can "pre-filter" them somehow?


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