Some aspects of generalized QR factorizations
Christopher C. Paige · 1990
Abstract We use the terminology generalized QR factorizations (GQR) to refer to a certain class of transformations that apply to two general matrices A (n x m) and B (n x p), but which correspond to the QR factorization of B-1 A in the case where B is square and non-singular. We define the GQR and related product QR factorization (PQR), and show how these may be reliably computed. By PQR we mean transformations applied to general A (n x m) and B (n x p) which correspond to the QR factorization of BT A. Some applications of the GQR are considered and standard forms of linear equations and equivalent optimization problems that often arise in such applications are examined. The GQR produces triangular matrices from each of A and B, and it is indicated how careful use of these leads to increased understanding and generalization of some classes of problem and their solutions.