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

Syntax
C#
Visual Basic
public double LSESolve([In] TMtx B, [In] TVec C, [In] TVec D, [In] TVec X);
Remarks

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

 

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  

 

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