dc.contributor.author Schreiber, Robert S. en_US dc.contributor.author Van Loan, Charles en_US dc.date.accessioned 2007-04-23T17:21:51Z dc.date.available 2007-04-23T17:21:51Z dc.date.issued 1987-09 en_US dc.identifier.citation http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR87-864 en_US dc.identifier.uri https://hdl.handle.net/1813/6704 dc.description.abstract A 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.extent 524587 bytes dc.format.extent 170980 bytes dc.format.mimetype application/pdf dc.format.mimetype application/postscript dc.language.iso en_US en_US dc.publisher Cornell University en_US dc.subject computer science en_US dc.subject technical report en_US dc.title A Storage Efficient WY Representation for Products of Householder Transformations en_US dc.type technical report en_US
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