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We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 × 2 pivoting for stability. This code, called MAST, is in HSL 2002 and supersedes the well used HSL code MA27. We describe some of the implementation details and emphasize the novel features of MAST. These include restart facilities, matrix modification, partial solution for matrix factors, solution of multiple right-hand sides, and iterative refinement and error analysis. The code is written in Fortran 77, but there are additional facilities within a Fortran 90 implementation that include the ability to identify and change pivots. Several of these facilities have been developed particularly to support optimization applications, and we illustrate the performance of the code on problems arising therefrom. [ABSTRACT FROM AUTHOR]

Describes the Basic Linear Algebra Subprograms (BLAS) for sparse matrices. Goal of the Sparse BLAS standard; Functionalities of the BLAS for dense matrix and vector operations; Procedure for the use of the Sparse BLAS; Routines for the creation of sparse matrices.

Discusses the interface design for the Sparse Basic Linear Algebra Subprograms, the kernels in the standard from the BLAS Technical Forum that are concerned with unstructured sparse matrices. Different ways of storing and accessing the nonzero entries of the sparse matrix; Details of handle-based generic interface; Representation of sparse vectors.

Provides a study and comparison of two state-of-the-art direct solvers for large sparse sets of linear equations on large-square memory-distributed computers. Description of the main algorithmic features of the two solvers; Comparison of their performance characteristics; Impact on both solvers of the preprocessing of the matrix.

Describes the design and implementation of a frontal code called MA62 for the solution of sparse positive-definite symmetric systems of linear finite-element equations. Main features and phases of the MA62 code; Use of high-level Basic Linear Algebra Subprograms for the MA62 code's numerical factorization; Comparison between the MA42 and other Harwell Subroutine Library codes.

Presents information on a study which discussed the organization of frontal matrices in multifrontal methods for the solution of large sparse sets of unsymmetric linear equations. Frontal matrices stored during the factorization; Need for extra work to sum the frontal matrices together; Effectiveness of a combined unifrontal/multifrontal algorithm.

Proposes a set of Level 3 Basic Linear Algebra Subprograms and associated kernels for sparse matrices. Design, implementation and use of subprograms full matrix multiplication; Routines for permuting, data checking, changing of data format and performing diagonal scaling of matrices; Use of Fortran 77.