Direct Methods for Sparse Matrices

I. S. (Iain) Duff is an STFC Senior Fellow in the Scientific Computing Department at the STFC Rutherford Appleton Laboratory in Oxfordshire, England. He is also the Scientific Advisor for the Parallel Algorithms Group at CERFACS in Toulouse and is a Visiting Professor of Mathematics at the University of Strathclyde.J. K. (John) Reid is an Honorary Scientist at the STFC Rutherford Appleton Laboratory in Oxfordshire, England. He is also a Visiting Professor at the Shrivenham Campus of Cranfield University and is Convener of the ISO/IEC Fortran Committee. A. M. (Al) Erisman is the Executive in Residence in the School of Business, Government, and Economics at Seattle Pacific University and is executive editor of Ethix magazine (), which he co-founded with a colleague in 1998. Over the past 15 years he has lectured on five continents in areas of business, technology, mathematics, ethics, faith, and economic development.

• 1: Introduction2: Sparse matrices: storage schemes and simple operations3: Gaussian elimination for dense matrices: the algebraic problem4: Gaussian elimination for dense matrices: numerical considerations5: Gaussian elimination for sparse matrices: an introduction6: Reduction to block triangular form7: Local pivotal strategies for sparse matrices8: Ordering sparse matrices for band solution9: Orderings based on dissection10: Implementing Gaussian elimination without symbolic factorize11: Implementing Gaussian elimination with symbolic factorize12: Gaussian elimination using trees13: Graphs for symmetric and unsymmetric matrices14: The SOLVE phase15: Other sparsity-oriented issuesA: Matrix and vector normsB: Pictures of sparse matricesC: Solutions to selected exercises

This is a thorough and thoughtful revision of a classic text, bringing it up to date with respect to subsequent developments in the field whilst retaining the qualities of the first edition.