The DOI matches its Crossref record, with a small difference in title or year.
The WY Representation for Products of Householder Matrices
Abstract
A new way to represent products of Householder matrices is given that makes a typical Householder matrix algorithm rich in matrix-matrix multiplication. This is very desirable in that matrix-matrix multiplication is the operation of choice for an increasing number of important high performance computers. We tested the new representation by using it to compute the QR factorization on the FPS-164/MAX. Preliminary results indicate that it is a very efficient way to organize Householder computations.
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In the citing paper
“By absorbing cumulative channel-wise decay into the rank-one erase factors, the recurrence admits a compact WY form with the same high-level chunkwise structure used by efficient delta-rule kernels [14, 15, 16, 17].”
From Gated DeltaNet-2: Decoupling Erase and Write in Linear Attention (2026) · cites this paper as [14]
In the citing paper
“KDAlets each key channel decay at its own rate and retains the efficient WY-based chunkwise algorithm of DeltaNet [10, 14].”
From Gated DeltaNet-2: Decoupling Erase and Write in Linear Attention (2026) · cites this paper as [14]
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No references could be resolved yet.
Research works printed but not linked: 10
- 10.1016/0045-7825(76)90032-3 · DOI
- 10.1137/1.9781611971811 · DOI
- 10.1145/1271.319413 · DOI
- 10.1137/1026003 · DOI
- Golub G. H., 1983, Matrix computations
- D. Madura, R. Broussard, D. Strickland, FPS-164 MAX: parallel multiprocessing for linear algebra operation, Proc.1985 Array Processing Conference, New Orleans, 1985, 33–50
- 10.1007/BF02162505 · DOI
- Smith B. T., 1970, Matrix Eigensystem Routines: EISPACK Guide
- 10.1007/BF01396447 · DOI
- 10.1007/BF01389653 · DOI
Cited by
Sorted by citations
The LINPACK Benchmark: past, present and future
Dongarra, J. J., Luszczek, P., & Petitet, A. (2003) · Concurrency and Computation: Practice and Experience · doi:10.1002/cpe.728 · Cited by 813
Kimi Linear: An Expressive, Efficient Attention Architecture
Kimi Team, Zhang, Y., Lin, Z., Yao, X., Hu, J., Meng, F., Liu, C., Men, X., Yang, S., Li, Z., et al. (2025) · arXiv · doi:10.48550/arxiv.2510.26692 · Cited by 1
Gated DeltaNet-2: Decoupling Erase and Write in Linear Attention
Hatamizadeh, A., Choi, Y., & Kautz, J. (2026) · arXiv
“With D 𝑡 = Diag( 𝛼 𝑡 ) , its update can be written as KDA lets each key channel decay at its own rate and retains the efficient WY-based chunkwise algorithm of DeltaNet [10, 14].”
Metadata
- Authors
- Bischof, C., & Van Loan, C.
- Affiliations
- Cornell University (US)
- ORCID
- Bischof, Christian
- Venue
- SIAM Journal on Scientific and Statistical Computing
- Published
- 1987-01
- Volume
- 8
- Issue
- 1
- Pages
- s2-s13
- ISSN
- 0196-5204 (ISSN-L)
- 2168-3417
- OpenAlex
- W2073216164
- Cited by
- 295
- References
- 0
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 8 · 2023: 3 · 2022: 6 · 2021: 4 · 2020: 5 · 2019: 8 · 2018: 11 · 2017: 8 · 2016: 4 · 2015: 13 · 2014: 6 · 2013: 12 · 2012: 10
- FWCI
- 20.90
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- SIAM Journal on Scientific and Statistical Computing (publishedVersion)
- eCommons (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Computer Science › Hardware and Architecture › Parallel Computing and Optimization Techniques
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Numerical Methods and Algorithms
- Keywords
- product representation, matrix-matrix multiplication, QR decomposition, high-performance computing, vector processors
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