This repository contains code for the paper "Fiber product homotopy method for multiparameter eigenvalue problems".

Our homotopy method tracks several copies of the eigenvalue λ; they should all converge to the same value if our method performs correctly.

The λi1 coordinates of all eight paths for t ∈ [0.95, 1] and i = 1, 2, 3.	The λi1 coordinates of the path highlighted in the left panel for t ∈ [0, 1] and i = 1, 2, 3.

• MATLAB, this folder contains our MATLAB implementation of the fiber product homotopy method, including the parallelization version. To compare with the Delta method, you will need to install the MATLAB package MultiEigPar first.
• Bertini, this folder contains Macaulay2 implementation for running both the fiber product homotopy method and the diagonal coefficient homotopy method on Bertini.

All our experiments are done on RCC Midway with 28 cpu cores and 56G memory.