Solving sparse linear systems: taking the direct approach

In this paper, we explore the importance of ordering when solving large, sparse systems of linear equations. Examples are drawn from the solution of partial differential equations; such problems are a prime source of such linear systems. Nothing that we do is specific to these problems, however, and you might prefer to work with a matrix from a standard test set (for example, 'wathen' from Matlab's gallery function or a matrix from the Matrix Market at http://math.nist.gov/MatrixMarket/) or a matrix of particular interest in your work.