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.
%0 Journal Article
%1 gill1974methods
%A Gill, P. E.
%A Golub, G. H.
%A Murray, W.
%A Saunders, M. A.
%D 1974
%J Math. Comp.
%K Cholesky_decomposition low_rank_update matrices numerical_methods
%P 505--535
%T Methods for modifying matrix factorizations
%U http://lapmal.epfl.ch/papers/cholupdate.pdf
%V 28
%X 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.
@article{gill1974methods,
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.
},
added-at = {2012-02-28T20:45:41.000+0100},
author = {Gill, P. E. and Golub, G. H. and Murray, W. and Saunders, M. A.},
biburl = {https://www.bibsonomy.org/bibtex/23acab4af30d315658b42ac602507dd62/peter.ralph},
fjournal = {Mathematics of Computation},
interhash = {ba07a2ed71df0108b41c8003b68dcb08},
intrahash = {3acab4af30d315658b42ac602507dd62},
issn = {0025-5718},
journal = {Math. Comp.},
keywords = {Cholesky_decomposition low_rank_update matrices numerical_methods},
mrclass = {65F05},
mrnumber = {0343558 (49 \#8299)},
mrreviewer = {L. W. Ehrlich},
pages = {505--535},
timestamp = {2012-02-28T20:45:41.000+0100},
title = {Methods for modifying matrix factorizations},
url = {http://lapmal.epfl.ch/papers/cholupdate.pdf},
volume = 28,
year = 1974
}