A block orthogonalization procedure with constant synchronizationrequirements
Journal Article
·
· SIAM Journal on Scientific Computing
OSTI ID:861995
We propose an alternative orthonormalization method that computes the orthonormal basis from the right singular vectors of a matrix. Its advantage are: (a) all operations are matrix-matrix multiplications and thus cache-efficient, (b) only one synchronization point is required in parallel implementations, (c) could be more stable than Gram-Schmidt. In addition, we consider the problem of incremental orthonormalization where a block of vectors is orthonormalized against a previously orthonormal set of vectors and among itself. We solve this problem by alternating iteratively between a phase of Gram-Schmidt and a phase of the new method. We provide error analysis and use it to derive bounds on how accurately the two successive orthonormalization phases should be performed to minimize total work performed. Our experiments confirm the favorable numerical behavior of the new method and its effectiveness on modern parallel computers.
- Research Organization:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
- Sponsoring Organization:
- USDOE Director, Office of Science. Office of AdvancedScientific Computing Research. Mathematical, Information, andComputational Sciences Division
- DOE Contract Number:
- AC02-05CH11231
- OSTI ID:
- 861995
- Report Number(s):
- LBNL--45577
- Journal Information:
- SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 6 Vol. 23; ISSN 1064-8275; ISSN SJOCE3
- Country of Publication:
- United States
- Language:
- English
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