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Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement.

Ondrej Slučiak1, Hana Straková2, Markus Rupp1

  • 1TU Wien, Institute of Telecommunications, Gusshausstrasse 25/E389, Vienna, 1040 Austria.

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|August 16, 2016
PubMed
Summary
This summary is machine-generated.

We developed a new distributed QR factorization algorithm for wireless sensor networks. This method offers a trade-off between speed and accuracy with fewer messages than current approaches.

Keywords:
Distributed processingGram-Schmidt orthogonalizationQR factorization

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Area of Science:

  • Distributed computing
  • Numerical analysis
  • Wireless sensor networks

Background:

  • Orthogonalization is crucial for decentralized data processing in wireless sensor networks.
  • Existing distributed orthogonalization algorithms often face challenges with communication overhead and iterative refinement.

Purpose of the Study:

  • To introduce a novel distributed QR factorization algorithm for vector orthogonalization in decentralized wireless sensor networks.
  • To enhance efficiency and reduce communication costs compared to existing methods.

Main Methods:

  • The algorithm is based on classical Gram-Schmidt orthogonalization, with recursive reformulation of projections and inner products.
  • It computes all elements of the resulting Q and R matrices simultaneously, refining them iteratively.
  • Numerical properties, performance, and robustness to link failures are thoroughly investigated.

Main Results:

  • The novel algorithm computes Q and R matrix elements simultaneously and refines them iteratively.
  • It demonstrates a trade-off between computation time and accuracy.
  • The number of transmitted messages is significantly reduced compared to state-of-the-art algorithms.

Conclusions:

  • The proposed distributed QR factorization algorithm offers an efficient and robust solution for vector orthogonalization in wireless sensor networks.
  • It provides a favorable balance between runtime, accuracy, and communication efficiency.
  • The algorithm's performance and robustness make it suitable for decentralized environments with potential link failures.