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December 10, 2025SMAI Journal of Computational MathematicsOpen Access

Exact discretization, tight frames and recovery via D -optimal designs

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Authors

FBFelix BartelCatholic University of Eichstätt-IngolstadtLKLutz KämmererChemnitz University of TechnologyKPKateryna PozharskaNational Academy of Sciences of Ukraine

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Overview

This work demonstrates precise quadrature and interpolation recovery in complex-valued functions via Gramian matrix, suggesting effective statistical designs.

Key Points

  • This research aims to explore D-optimal designs for effective experimental setups and accurate function recovery.
  • Maximizing determinants of Gramian matrices for constructing tight frames.
  • Using numerical analysis for quadrature and interpolation.
  • Applying results to the L2-norm of complex-valued functions and RKHS.
  • Reconstruction of functions shows effective subsampling of the L2-norm with specific points and weights.
  • Numerical experiments confirm the sharpness of the results regarding function recovery.

Cite This Study

Bartel et al. (2025) studied this question.

synapsesocial.com/papers/69401b312d562116f28f7c04https://doi.org/10.5802/smai-jcm.136
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