| Synopsis
| Least Squares approximation using the best sum of independent variables.
LSBestSum finds the best pair of variables which can be replaced by
their sum. This pair is best in the sense of increasing the norm of
the residuals by the least amount.
Problem: Given a matrix of A (dim n x m) and a vector b (dim n), we want
to find a vector x (dim m) such that Ax ~ b, where x has two values
which are identical. This approximation is in the least squares
sense, i.e. ||Ax-b||^2 is minimum.
The calling arguments are:
AtA is a matrix (dim m x m) which is the product A^t * A
btA is a vector (dim m) which is the product b^t * A
btb is the norm squared of b, i.e. b^t * b
Output: The output is a list with three values: [i,j,norm], where
i and j are integers and are the indices of the variables which
are replaced by their sum.
norm is the value of the norm of the residuals with this sum,
i.e. norm = ||Ax-b||^2
See Also: ?LSBestSumDelete ?LSBestDelete |