*This week, Katie and Paul are blogging from the Heidelberg Laureate Forum – a week-long maths conference where current young researchers in maths and computer science can meet and hear talks by top-level prize-winning researchers. For more information about the HLF, visit the Heidelberg Laureate Forum website.*

One of the more technical lectures at the HLF so far was given by Daniel Spielman, on the Approximate Gaussian Elimination algorithm his research group has produced, and how it differs from traditional Gaussian Elimination. So what is Gaussian Elimination?