Linear Least Squares Computations
We have other methods that, while more costly, are more robust in the face of rounding errors. The other methods arrive at xLS by a different route. Recall that the normal equations were a result of requiring that b− Ax be orthogonal (normal) to the subspace S = ColSp(A). That is another way of saying that Ax is the orthogonal projection of b onto S. The solution to the normal equations is therefore the solution to the rectangular, but consistent, linear system