Fast Programs for Big Problems
John Burkardt
Department of Scientific Computing
Florida State University
27/29 September 2011

Modern computing involves solving big problems.  
This means that CPU time, efficiency, performance monitoring,
and algorithmic scaling are important.  

This talk will give a simple overview of these questions,
using examples written in MATLAB.  We will start with the
simple question of measuring program "speed", how to look
for portions of a program that are consuming the most time,
and strategies for speeding up such regions.

We will look at a simple case study in which a computer
mesh has been computed, and it is now desired to construct
a list of the three triangles that are immediate neighbors
of a given triangle.  A simple search can carry out this
calculation on a small problem, but for a problem involving 
just 64,000 elements, it will take ``forever''.  

We will then look at complexity, a simple measure of the
relationship between the problem size N and the amount of
work W required to produce an answer.  Algorithms that can
be used for large problems must severely control the growth
in W as a function of N.  We will look at some typical
computations and discuss their complexities.

I hope this talk introduces you to the idea that sometimes
the size of a problem becomes an important factor in the
approach to its solution.