Abstracts: Iain Duff
In the early 1980's, John Reid and I worked on the development of a class of direct methods for solving sparse linear systems. Although the concept was already present in early research, we developed this in the context of general sparse systems and so can be credited with introducing multifrontal methods to the numerical analysis community.
In this talk, I discuss the origins of the multifrontal method and summarize the main contributions of our early papers, noting in particular how this early work anticipated later development to the extent that some of the ideas in our papers have been rediscovered many times since then.
I then sketch the subsequent development of multifrontal methods and show how they are now established as one of the major approaches to the direct solution of sparse linear equations.
Multifrontal methods can be viewed as a generalization of frontal methods. We briefly review the range of software implementing both frontal and multifrontal methods in HSL.