This project shows a demo of the algorithm of the a posteriori error estimation for eigenvector of eigenvalue problems, such as, the matrix eigenvalue problem, the Laplacian eigenvalue problem.



  • DEMO

Algorithm for a posteriori error estimation of eigenvectors

We consdier four eigenvalue problems with the aim to provide explicit estimation of the eigenvectors for each eigenvalue problem.

Directory description:

  • Matrix_eigenprob: The eigenvalue problem of matrices.
  • Square_domain: The Laplacian eigenvalue problem over a square domain.
  • L_shaped_domain: The Laplacian eigenvalue problem over an L-shaped domain.
  • Dumbbell_domain: The Laplacian eigenvalue problem over a dumbbell-shaped domain.

How to run the code?

Start the demo at this page and the system will start a virtual machine to load Jupyter notebook, where the .ipynb file can be opened and executed.


The theoretical description of the algorithm can be found in the paper below:

  • Xuefeng Liu, Tomáš Vejchodský, Fully computable a posteriori error bounds for eigenfunctions, https://arxiv.org/abs/1904.07903

Contact for demo codes: Xuefeng LIU (xfliu.math@gmail.com)

About the directory

Folders or files beginning with a dot are not displayed by default.

Virtual Machine Setting


You are starting the virtual machine as a visitor to current project. As a visitor, you can change files in the booted virtual machine, but the changed files will be aborted when the server is shut down.

(Please login first to start the virtual machine.)

About Machine Type

The machine with type as "n1-standard-1" has 1 CPU Core and 4GB memory. The Google app compute engine provides a detailed guide of the machine type. For more detailed information, please refer to More detail.
If you need a high-spec machine type, please contact the site manager.