Zhengbo Zhou

Zhengbo Zhou

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A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.

Pages

Posts

The Jacobi algorithm for eigenvalues

2 minute read

Published:

Jacobi algorithm

Given a symmetric $A \in \mathbb{R}^{n\times n}$, the Jacobi algorithm produces a sequence of orthogonally similar matrices $A_{k+1} = J_{k}^{T} A_{k} J_{k}$ for $k = 1,2,\dots$, $A_{1} = A$, and $J_{k}$ are the carefully constructed Jacobi rotations. In fact, the Jacobi rotation is the same as the Givens rotation, but we give the credit to the inventor, Carl G. J. Jacobi. Read more

A MATLAB function to generate random symmetric matrix

3 minute read

Published:

The MATLAB builtin function gallery('randsvd',...) can only generate a random matrix or a symmetric positive definite matrix. However, sometimes, we need to test our algorithms for symmetric matrices. Although you can get a symmetric matrix by A = randn(n); A = A + A';, it would be nice to inherit the features from gallery('randsvd'), such as the ability to control the distributions of the singular values. The attached code achieves such desire by

  • first, generate singular values,
  • then construct a random orthogonal matrix using qmult, and
  • finally multiply the orthogonal matrix at both sides of the diagonal matrix that contains these singular values.
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portfolio

publications

Paper Title Number 4

Published in GitHub Journal of Bugs, 2024

This paper is about fixing template issue #693. Read more

Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).
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talks

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

This is a description of a teaching experience. You can use markdown like any other post. Read more

Teaching experience 2

Workshop, University 1, Department, 2015

This is a description of a teaching experience. You can use markdown like any other post. Read more