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.
http://i.stanford.edu/pub/cstr/reports/cs/tr/72/322/CS-TR-72-322.pdf