Linear Algebra is an incredibly powerful tool. A joke among mathematicians is that the only way we can solve a hard problem is to boil it down to Linear Algebra¹. Harnessing the numerical power of Linear Algebra has been done via LAPACK for the last 40+ years.

In my …

After five years, I'm excited to say I've finished my PhD. I certainly learned a lot and met a lot of great people along the way.

One of the biggest lessons I learned was about myself: I need to say no more often. I continued to say yes, to side …

Caveat: I stopped using a Mac for my development machine way back in the fall of 2014. You probably shouldn't listen to me.

What Not to Do

The first rule of using Python on any operating system: don't use system Python. The OS relies on that Python, including the packages …

About a year ago, I was reading the Go source for computing $\log(x)$ and was very surprised by the implementation.¹

Even three years into a PhD in Applied Math (i.e. numerics), I still managed to learn something by diving in and trying …

Finding zeros of any old function is a common task, and using Newton's method is one of the best tools for carrying out this task. I've even written an old post that used this method.

However, Newton's method loses some of it's luster around repeated roots. Consider the iteration