Mai is an app that I created with Jason, Brian, David, and John at our coding bootcamp. With Mai, you can post photos and share stories, much like Facebook and Instagram. Mai takes one step further by writing the stories for you.
- 3JS: For super awesome graphics
- D3: For data lovers
- Ember: For ambitious team projects
- React + Redux: For easy learning
- Node: For everything
Happy 2018 everyone!
How many of you like to eat, play, and most importantly, drink? (Hopefully, everyone!)
I helped create an app called LocALL. It gives 50,000 recommendations for short trips to eat, play, and drink and support local businesses in Austin. We can extend our app to cover ~400 metropolitan cities in the US and create 20 million recommendations. (Big data and machine learning!)
At the heart of our solution is math. We used spherical geometry and probability to create simple, fast recommendations.
Let’s look at one more way to solve the equation . We assume that is nonsingular, and define the -th Krylov subspace as follows:
Krylov subspace methods are efficient and popular iterative methods for solving large, sparse linear systems. When is symmetric, positive definite (SPD), i.e.
we can use a Krylov subspace method called Conjugate Gradient (CG).
Today, let’s find out how CG works and use it to solve 2D Poisson’s equation.
Last time, we looked at 2D Poisson’s equation and discussed how to arrive at a matrix equation using the finite difference method. The matrix, which represents the discrete Laplace operator, is sparse, so we can use an iterative method to solve the equation efficiently.
Today, we will look at Jacobi, Gauss-Seidel, Successive Over-Relaxation (SOR), and Symmetric SOR (SSOR), and a couple of related techniques—red-black ordering and Chebyshev acceleration. In addition, we will analyze the convergence of each method for the Poisson’s equation, both analytically and numerically.