Generalized QR factorization and its applications

The purpose of this paper is to reintroduce the generalized QR factorization with or without pivoting of two matrices A and B having the same number of rows. When B is square and nonsingular, the factorization implicity gives the orthogonal factorization of B^-1A. Continuing the work of Paige and Hammarling, we discuss the different forms of the factorization from the point of view of general-purpose software development. In addition, we demonstrate the applications of the GQR factorization in solving the linear equality-constrained least-squares problem and the generalized linear regression problem, and in estimating the conditioning of these problems.