Complete Orthogonal Factorization

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Complete Orthogonal Factorization

The QR factorization with column pivoting does not enable us to compute a minimum norm solution to a rank-deficient linear least squares problem,   unless . However, by applying further orthogonal (or unitary) transformations  from the right to the upper trapezoidal matrix , using the routine xTZRQF, can be eliminated:     

This gives the complete orthogonal factorization 

from which the minimum norm solution  can be obtained as

Tue Nov 29 14:03:33 EST 1994