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Column reduced digital nets.

Vishnupriya Anupindi1, Peter Kritzer1

  • 1RICAM, Austrian Academy of Sciences, Altenbergerstr. 69, 4040 Linz, Austria.

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Summary
This summary is machine-generated.

This study introduces a new algorithm for faster matrix-vector products using column reduced digital nets in quasi-Monte Carlo (QMC) methods. This approach enhances computational speed and simplifies error analysis for QMC integration nodes.

Keywords:
Digital netDigital sequenceNumerical integrationReduced digital net

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Area of Science:

  • Numerical Analysis
  • Computational Mathematics
  • Quasi-Monte Carlo Methods

Background:

  • Digital nets efficiently generate integration nodes for quasi-Monte Carlo (QMC) rules.
  • Accelerating matrix-vector products with QMC nodes is crucial for applications like uncertainty quantification.
  • Prior work utilized reduced lattices and row reduced digital nets for speed-up.

Purpose of the Study:

  • To develop a novel matrix-vector multiplication algorithm for QMC.
  • To exploit the repetitive structure of column reduced digital nets.
  • To improve upon existing methods for fast QMC matrix-vector products.

Main Methods:

  • Proposed a new multiplication algorithm leveraging column reduced digital nets.
  • Developed an upper bound for the quality parameter of column reduced digital nets.
  • Conducted numerical tests to validate the algorithm's efficiency.

Main Results:

  • The new algorithm exploits the structure of column reduced digital nets for faster matrix-vector products.
  • This method facilitates error analysis compared to previous approaches.
  • Numerical tests demonstrate the efficiency of the proposed algorithm.

Conclusions:

  • The developed algorithm offers an efficient alternative for matrix-vector products in QMC.
  • Exploiting column reduced digital nets provides advantages in speed and error analysis.
  • The findings contribute to the advancement of computational methods in QMC applications.