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On the Stability of Sequential Updates and Downdates

dc.contributor.authorStewart, G. W.en_US
dc.description.abstractThe updating and downdating of QR decompositions has important applications in a number of areas. There is essentially one standard updating algorithm, based on plane rotations, which is backwards stable. Three downdating algorithms have been treated in the literature: the LINPACK algorithm, the method of hyperbolic transformations, and Chambers' algorithm. Although none of these algorithms is backwards stable, the first and third satisfy a relational stability condition. In this paper, it is shown that relational stability extends to a sequence of updates and downdates. In consequence, other things being equal, if the final decomposition in the sequence is well conditioned, it will be accurately computed, even though intermediate decompositions may be almost completely inaccurate. These results are also applied to the two-sided orthogonal decompositions, such as the URV decomposition. (Also cross-referenced as UMIACS-TR-94-30)en_US
dc.format.extent180256 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3238en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-94-30en_US
dc.titleOn the Stability of Sequential Updates and Downdatesen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US

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