Generalized QR factorization and its applications

  • Anderson E
  • Bai Z
  • Dongarra J
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Abstract

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. © 1992.

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Authors

  • E. Anderson

  • Z. Bai

  • J. Dongarra

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