Report Number: CS-TR-72-322
Institution: Stanford University, Department of Computer Science
Title: Methods for modifying matrix factorizations.
Author: Gill, Phillip E.
Author: Golub, Gene H.
Author: Murray, Walter A.
Author: Saunders, Michael A.
Date: November 1972
Abstract: In recent years several algorithms have appeared for
modifying the factors of a matrix following a rank-one
change. These methods have always been given in the context
of specific applications and this has probably inhibited
their use over a wider field. In this report several methods
are described for modifying Cholesky factors. Some of these
have been published previously while others appear for the
first time. In addition, a new algorithm is presented for
modifying the complete orthogonal factorization of a general
matrix, from which the conventional QR factors are obtained
as a special case. A uniform notation has been used and
emphasis has been placed on illustrating the similarity
between different methods.