TMtx.LSESolve Method

Solves the linear equality-constrained least squares (LSE).

Solves the linear equality-constrained least squares (LSE) problem:

minimize || c - A*x ||_2   subject to   B*x = d

where A is an M-by-N matrix, B is a P-by-N matrix, c is a given vector of length M, and d is a given vector of length P. The sign "_2", denotes Norm L2. It is assumed that P <= N <= M+P, and

rank(B) = P and  rank( (A) ) = N
                     ( (B) )

These conditions ensure that the LSE problem has a unique solution, which is obtained using a generalized RQ factorization of the matrices (B, A) given by

B = (0 R)*Q,   A = Z*T*Q

The function returns the residual sum of squares for the solution

References:

1.) Lapack v3.4 source code

2.) http://isites.harvard.edu/fs/docs/icb.topic774900.files/lec16.09.pdf

3.) http://www.cs.ucdavis.edu/~bai/publications/andersonbaidongarra92.pdf