PEVP_with_Taylor_and_Chebyshev

This repository contains MATLAB code to solve parametric eigenvalue problems with a Taylor or Chebyshev expansion. The code has been used for the numerical experiments in the paper “Solving the Parametric Eigenvalue Problem by Taylor Series and Chebyshev Expansion” by Thomas Mach and Melina Freitag.

A parametric eigenvalue problem has the form

A(mu) v(mu) = lambda(mu) v(mu),

with A(mu) given. The code computes approximations for eigenpairs (lambda(mu),v(mu)).

The code was tested with MATLAB R2020b and R2021b in combination with the latest release of Chebfun (v.5.7.0). The Chebfun package is available on github at https://github.com/chebfun/chebfun. Chebfun is used to represent the matrix A(mu) in some of the examples.

Authors

• Thomas Mach, University of Potsdam
• Melina Freitag, University of Potsdam

Publication

• Thomas Mach, Melina Freitag: Solving the Parametric Eigenvalue Problem by Taylor Series and Chebyshev Expansion, in preparation.

The data to generate all figures of the paper can be generated by running the scrip

generate_all_data_for_all_figures.m

• Melina A. Freitag , Pavel Kríž , Thomas Mach, and Jan Martin Nicolaus: Can one hear the depth of the water?

The data is generated with the script

experiments_pamm.m

Installation