LQ Factorization

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LQ Factorization

The LQ factorization  is given by

where L is m-by-m lower triangular, Q is n-by-n orthogonal (or unitary), consists of the first m rows of Q, and the remaining n - m rows.

This factorization is computed by the routine xGELQF, and again Q is      represented as a product of elementary reflectors; xORGLQ      (or xUNGLQ   in the complex case) can generate all or part of Q, and xORMLQ   (or xUNMLQ   ) can pre- or post-multiply a given matrix by Q or ( if Q is complex).

The LQ factorization of A is essentially the same as the QR factorization of ( if A is complex), since

The LQ factorization may be used to find a minimum norm solution  of an underdetermined  system of linear equations Ax = b where A is m-by-n with m < n and has rank m. The solution is given by

and may be computed by calls to xTRTRS and xORMLQ.        

Tue Nov 29 14:03:33 EST 1994