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Rational approximation with multidimensional scattered data.

Xu-Guang Hu1, Tak-San Ho, Herschel Rabitz

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
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This study introduces a new weighted least-squares method for accurate multidimensional scattered data interpolation. The efficient rational approximation scheme demonstrates high performance in complex model systems.

Area of Science:

  • Computational Mathematics
  • Numerical Analysis
  • Scientific Computing

Background:

  • Multidimensional scattered data interpolation is crucial for solving complex scientific problems.
  • Existing methods often struggle with accuracy and efficiency on irregular grids.
  • Quantum fluid dynamics simulations require robust function approximation techniques.

Purpose of the Study:

  • To develop and implement accurate and efficient rational approximation schemes for multidimensional scattered data.
  • To address the need for function approximation using irregular grids in scientific computing.
  • To present a novel weighted least-squares procedure with domain decomposition.

Main Methods:

  • Formulation of two specific representations of the rational approximation method.

Related Experiment Videos

  • Implementation of corresponding algorithms for data interpolation.
  • Application of a weighted least-squares procedure incorporating domain decomposition.

    • Main Results:

    • Numerical tests on three- and six-dimensional model systems were conducted.
    • The implemented algorithms demonstrated high efficiency.
    • The results confirmed the high accuracy of the proposed method.

    Conclusions:

    • The novel weighted least-squares procedure provides an accurate and efficient solution for multidimensional scattered data interpolation.
    • The method is particularly suitable for irregular grids and has potential applications in quantum fluid dynamics and other physical sciences.
    • The developed algorithms are robust and perform well on complex, high-dimensional systems.