Sparse matrix orderings: it's child's play! Or is it?

Sparse matrices occur in numerical simulations throughout science and engineering. In particular, it is often desirable to solve systems of the form Ax=b, where A is a sparse matrix with 100,000+ rows and columns. The order that the rows and columns occur in can have a dramatic effect on the viability of a direct solver e.g., the time taken to find x, the amount of memory needed, the quality of x,... We shall consider symmetric matrices and, with the help of playdough, explore how best to order the rows/columns using a nested dissection strategy. Starting with a straightforward strategy, we will discover the pitfalls and develop an adaptive strategy with the aim of coping with a large variety of sparse matrix structures.

Some of the talk will involve the audience playing with playdough, so bring your inner child along with you!