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Generalized RQ factorization

    The generalized RQ (GRQ) factorization of an m-by-n matrix A and a p-by-n matrix B is given by the pair of factorizations
where Q and Z are respectively n-by-n and p-by-p orthogonal matrices (or unitary matrices if A and B are complex). R has the form
where tex2html_wrap_inline13555 or tex2html_wrap_inline13795 is upper triangular. T has the form
where tex2html_wrap_inline13799 is upper triangular.

Note that if B is square and nonsingular, the GRQ factorization of A and B implicitly gives the RQ factorization of the matrix tex2html_wrap_inline13809:
without explicitly computing the matrix inverse tex2html_wrap_inline13720 or the product tex2html_wrap_inline13809.

The routine PxGGRQF computes the GRQ factorization       by computing first the RQ factorization of A and then the QR factorization of tex2html_wrap_inline13821. The orthogonal (or unitary) matrices Q and Z can be formed explicitly or can be used just to multiply another given matrix in the same way as the orthogonal (or unitary) matrix in the RQ factorization (see section 3.3.2).

Susan Blackford
Tue May 13 09:21:01 EDT 1997