Convergence theory for Hermite approximations under adaptive coordinate transformations

This repository contains source code and results of calculations accompanying the manuscript:

Y. Saleh: Convergence theory for Hermite approximations under adaptive coordinate transformations. arXiv:2604.16975 (2026). DOI:10.48550.

Contents

The experiments pertaining to interpolation problems are provided in Hermite_approx.ipynb, Hermite_lin_approx.ipynb, Hermite_iResNet_approx.ipynb and Hermite_sublin_approx.ipynb for Hermite approximations employing identity, linear, iResNet, and power-law transformations, respectively. The scripts save data in simulations_data.

In plot_results.ipynb, the simulation data are loaded and used to produce the figures of the manuscript.

The experiments pertaining to the Morse oscillator are provided in Morse_Hermite.ipynb, Morse_scaled_Hermite.ipynb, Morse_NF_Hermite.ipynb. Analysis is performed in Morse_analysis.py and results are plotted in plot_results_Morse.ipynb

Citation

If you use this code in your research, please cite:

Y. Saleh: Convergence theory for Hermite approximations under adaptive coordinate transformations. arXiv:2604.16975 (2026). DOI:10.48550.

@article{Saleh:arXiv2604:16975,
	author = {Saleh, Yahya},
	year   = {2026},
	journal= {arXiv preprint arXiv:2604.16975},
	title  = {Convergence theory for Hermite approximations under adaptive coordinate transformations},
	doi    = {https://doi.org/10.48550/arXiv.2604.16975},
  }

Contact

For questions or feedback, feel free to open an issue or reach out to the authors directly via yahya.saleh@mathmods.eu.