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- W2039778940 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 >> 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." @default.
- W2039778940 created "2016-06-24" @default.
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- W2039778940 date "1989-01-01" @default.
- W2039778940 modified "2023-09-26" @default.
- W2039778940 title "A Storage-Efficient $WY$ Representation for Products of Householder Transformations" @default.
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- W2039778940 doi "https://doi.org/10.1137/0910005" @default.
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