### 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.

Public

• 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)

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

## Virtual Machine Setting

#### Warning!

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.