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具有同步元素细化的分布式Gram-Schmidt正交化

Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement.

作者信息

Slučiak Ondrej, Straková Hana, Rupp Markus, Gansterer Wilfried

机构信息

TU Wien, Institute of Telecommunications, Gusshausstrasse 25/E389, Vienna, 1040 Austria.

University of Vienna, Faculty of Computer Science, Theory and Applications of Algorithms, Währingerstrasse 29, Vienna, 1090 Austria.

出版信息

EURASIP J Adv Signal Process. 2016;2016:25. doi: 10.1186/s13634-016-0322-6. Epub 2016 Feb 24.

DOI:10.1186/s13634-016-0322-6
PMID:27525005
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4962951/
Abstract

We present a novel distributed QR factorization algorithm for orthogonalizing a set of vectors in a decentralized wireless sensor network. The algorithm is based on the classical Gram-Schmidt orthogonalization with all projections and inner products reformulated in a recursive manner. In contrast to existing distributed orthogonalization algorithms, all elements of the resulting matrices and are computed simultaneously and refined iteratively after each transmission. Thus, the algorithm allows a trade-off between run time and accuracy. Moreover, the number of transmitted messages is considerably smaller in comparison to state-of-the-art algorithms. We thoroughly study its numerical properties and performance from various aspects. We also investigate the algorithm's robustness to link failures and provide a comparison with existing distributed QR factorization algorithms in terms of communication cost and memory requirements.

摘要

我们提出了一种新颖的分布式QR分解算法，用于在分散式无线传感器网络中对一组向量进行正交化处理。该算法基于经典的Gram-Schmidt正交化方法，所有投影和内积都以递归方式重新表述。与现有的分布式正交化算法不同，所得矩阵的所有元素同时进行计算，并在每次传输后进行迭代细化。因此，该算法允许在运行时间和准确性之间进行权衡。此外，与现有算法相比，传输的消息数量要少得多。我们从各个方面深入研究了其数值特性和性能。我们还研究了该算法对链路故障的鲁棒性，并在通信成本和内存需求方面与现有的分布式QR分解算法进行了比较。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/b45218dbc1ff/13634_2016_322_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/9b1099894181/13634_2016_322_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/1b9a4abf1334/13634_2016_322_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/cbebb9667e1b/13634_2016_322_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/abfe813ebb7c/13634_2016_322_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/f85abed754c7/13634_2016_322_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/414036c729af/13634_2016_322_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/e1159bceb641/13634_2016_322_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/a60f2cda29c9/13634_2016_322_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/c5f1ca5a0614/13634_2016_322_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/8ae43b963e3f/13634_2016_322_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/21ab2e59c54b/13634_2016_322_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/b45218dbc1ff/13634_2016_322_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/9b1099894181/13634_2016_322_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/1b9a4abf1334/13634_2016_322_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/cbebb9667e1b/13634_2016_322_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/abfe813ebb7c/13634_2016_322_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/f85abed754c7/13634_2016_322_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/414036c729af/13634_2016_322_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/e1159bceb641/13634_2016_322_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/a60f2cda29c9/13634_2016_322_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/c5f1ca5a0614/13634_2016_322_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/8ae43b963e3f/13634_2016_322_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/21ab2e59c54b/13634_2016_322_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8aec/4962951/b45218dbc1ff/13634_2016_322_Fig12_HTML.jpg

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