An introduction to chordal graphs and clique trees. - Cutting down on fill using nested dissection: Provably good elimination orderings. - Automatic Mesh Partitioning. - Structural representations of Schur complements in sparse matrices. - Irreducibility and primitivity of Perron complements: Application of the compressed directed graph. - Predicting structure in nonsymmetric sparse matrix factorizations. - Highly parallel sparse triangular solution. - The fan-both family of column-based distributed Cholesky factorization algorithms. - Scalability of sparse direct solvers. - Sparse matrix factorization on SIMD parallel computers. - The efficient parallel iterative solution of large sparse linear systems. Language: English