Hello there!

Hello! My name is Timothy (but my friends usually call me Timo) and I am a PhD student in mathematics at the National University of Singapore (NUS). As I was beginning my PhD studies in NUS, I had decided to set up a personal page, to serve as a way to introduce myself and my work to others, as well as to have a place to write my ideas.

This webpage is a work in progress! There are many things that I want to do, but I am not familiar enough with Hugo (the content management system) or the theme to implement them immediately. For example, I am trying to set up a comment system with utterances, and I would like to tweak the colours a little.

If you would like to contact me for some reason, you can do so via my email at timothywan dot ky at gmail dot com. Enjoy your stay!

A Simple Randomized Matrix Multiplication Algorithm 2

The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. – Sir Francis Galton This post is the continuation of the previous post over here. Last Time In the previous post, we began the analysis of a randomized matrix multiplication algorithm. We managed to prove that the output of the algorithm gives us our product $AB$ in expectation, and furthermore, that the expected squared deviation $\mathbb{E}[\|D-AB\|_F^2]$ satisfies ...

A Simple Randomized Matrix Multiplication Algorithm 1

千里之行，始於足下。 [The journey of a thousand miles begins with a simple step.] – Lao Tzu Introduction We all have to start somewhere, and I have decided to start the blog with something simple, that most people in the quantitative sciences would have to deal with at some point in their lives: matrix multiplication. Performing matrix multiplication fast is important for many applications, like machine learning or numerical methods. We will consider matrices (square of order $n$, for simplicity) $A=(a_{ij})_{i,j=1}^n$, and $B=(b_{ij})_{i,j=1}^n$, think about ways to evaluate $AB$. The simplest, most naive algorithm would be as follows: ...