%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 }