Data-driven optimal approximation on Hardy spaces in simply connected domains

This repository contains code for the manuscript

A. Borghi, T. Breiten, Data-driven optimal approximation on Hardy spaces in simply connected domains, ArXiv (2025)

For the experiments to work chebfun needs to be installed.

The algorithm described in the manuscript can be found in code/functions/algorithm1.m. The functions fdm_2d_matrix.m and fdm_2d_vector.m can be found in the LYAPACK toolbox (see also here). In addition, the clambed beam example can be found in

Niconet e.V., SLICOT - Subroutine Library in Systems and Control Theory, http://www.slicot.org

To get the results showed in the paper, the following files can be executed in the code folder:

(Plots of the conformal mappings and reflections)

• mappings.m

(Heat equation example)

• mobius_E2D_heat.m

(Backward differentiation methods examples)

• BDF2_test_disc.m
• BDF4_test_disc.m