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Related Experiment Video

Updated: Sep 29, 2025

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An Efficient, Memory-Saving Approach for the Loewner Framework.

Davide Palitta1, Sanda Lefteriu2

  • 1Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, 39106 Magdeburg, Germany.

Journal of Scientific Computing
|March 21, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method to efficiently compute rational models using the Loewner framework. By exploiting the Cauchy-like structure of Loewner matrices, it reduces computational costs and memory requirements for large datasets.

Keywords:
Cauchy-like matricesData-driven model order reductionHSS matricesLoewner framework

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Area of Science:

  • Numerical Analysis
  • Model Order Reduction
  • Data-Driven Modeling

Background:

  • The Loewner framework is a successful data-driven technique for model order reduction.
  • Loewner and shifted Loewner matrices are essential for rational model approximation.
  • Dense matrices in the Loewner framework cause computational and memory issues with large datasets.

Purpose of the Study:

  • To develop a computationally efficient and memory-saving approach for the Loewner framework.
  • To address the numerical difficulties associated with large, highly-sampled datasets.
  • To reduce the cost of computing accurate rational models.

Main Methods:

  • Exploiting the Cauchy-like structure of Loewner and shifted Loewner matrices.
  • Utilizing the hierarchically semiseparable (HSS) format.
  • Avoiding explicit allocation of large dense matrices.

Main Results:

  • A novel scheme for the Loewner framework with costs scaling linearly with the data set size (N).
  • Significant reduction in computational cost and memory requirements.
  • Accurate rational models are constructed while overcoming numerical limitations.

Conclusions:

  • The proposed method effectively overcomes the limitations of the traditional Loewner framework for large datasets.
  • Exploiting matrix structure offers a path to scalable model order reduction.
  • This approach enables the computation of accurate rational models in memory-constrained environments.