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dc.contributor.authorSchreiber, Robert S.en_US
dc.contributor.authorVan Loan, Charlesen_US
dc.date.accessioned2007-04-23T17:21:51Z
dc.date.available2007-04-23T17:21:51Z
dc.date.issued1987-09en_US
dc.identifier.citationhttp://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR87-864en_US
dc.identifier.urihttps://hdl.handle.net/1813/6704
dc.description.abstractA product $Q = P_{1} \cdots P_{r}$ of m-by-m Householder matrices can be written in the form $Q = I + WY^{T}$ where W and Y are each m-by-r. This is called the WY representation of Q. It is of interest when implementing Householder techniques in high-performance computing environments that "like" matrix-matrix multiplication. In this note we describe a storage efficient way to implement the WY representation. In particular, we show how the matrix Q can be expressed in the form $Q = I + YTY^{T}$ where $Y \epsilon R^{mxr}$ and $T \epsilon R^{rxr}$ with T upper triangular. Usually r less than less than m and so this "compact" WY representation requires less storage. When compared with the recent block-reflector strategy proposed by Schreiber and Parlett the new technique still has a storage advantage and involves a comparable amount of work.en_US
dc.format.extent524587 bytes
dc.format.extent170980 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/postscript
dc.language.isoen_USen_US
dc.publisherCornell Universityen_US
dc.subjectcomputer scienceen_US
dc.subjecttechnical reporten_US
dc.titleA Storage Efficient WY Representation for Products of Householder Transformationsen_US
dc.typetechnical reporten_US


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