Examples

We provide a collection of potential applications of the mLF package. Do not hesitate to suggest your (successfull) case to be included in this examples list. We also suggest to view the exhaustive arXiv report.

Getting started examples

• Rational function approximation
• Polynomial function approximation
• Irrational ReLU function approximation
• Tensor approximation
• Hilbert polynomial function
• Riemann $\zeta$ function
• Zolotarev 3rd (ratio) and 4th (sign) functions

Papers related examples

• Nonlinear eigenvalues approximation
  L. Balicki, M. Embree and S. Gugercin, A parametric Keldysh decomposition , arXiv:2601.01553, 2026.
• Porous irrational model approximation
  L. Schwoebel, C. Poussot-Vassal, D. Matignon, R. Roncen, E. Piot and P. Vuillemin, "Application of the multivariate Loewner Framework to the modelling of acoustic propagation in rigid-frame porous materials", in Proceedings of the Waves conference, Montréal, Canada, June, 2026.

Benchmark

We also suggest an exaustive benchmark set. The latter is documented and available with the below links:

• GitHub
• arXiv report