The Singular Value Decomposition is my favorite mathematical expression and also my favorite benchmark. It my favorite expression because it is so fundamental. If you are interested in finding out why, check out this great course on linear algebra from Gilbert Strang. If you watch one video from this course, watch this one.

There are some very cool examples of people using SVD for all sorts of stuff. I found these on Google: Sending Data from Mars and Cancer research.

The second reason I like the SVD is that it is a realistic computation. Given a matrix of size m*n it will require O(m*n)^2 operations. My LAPACK benchmark of a 10x10 matrix took 21800 floating point operations. It also requires full storage of U, V and S so it will require 3*(10*10*8) bytes or about 2.34 MB. Each operation is dependent on previous operations so you don't get artificially high floating point operation rates. I like the LAPACK SVD benchmark because it is a good measure of the peak real computational power of a computer.

So why am I even looking at the SVD? I am looking for some good ways to discuss optimization with people. If my mathematical calculations are on the order of 100,000,000 operations per second and the network time between requests is 30ms, then even an operation that takes 3 million operations is within the network noise, and will be imperceptible - even to the computer. Even my 800Mhz PIII gets 100Mflops!