Title

Author

xfliu

Description

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.

Properties

Public

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  • README
  • DIRECTORY
  • 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.

Reference

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

(Please login first to start the virtual machine.)

About file revision at virtual machine

For owner of the project, the file revised on the virtual machine will be saved after shutting down the server. As a visitor user, one can revise files in the booted virtual machine, but the revision will be aborted once the server is shut down.

About Machine Type

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.