Abstract :
Numerical linear algebra plays a vital role in all parts of computational mathematics, such as differential equations and optimization, and in many application areas, such as control theory. Large systems in these areas generally lead to linear algebra problems involving large sparse matrices (i.e., matrices of large dimension, but whose entries are mostly zeros). Efficient use of computer resources in solving such sparse matrix problems requires special techniques which have a distinct flavor compared to those used for dense matrices. We survey the current state of the art in sparse matrix computations, including the solution of systems of linear algebraic equations, linear least squares problems, and eigenvalue problems. Emphasis is placed on direct methods, but iterative methods are also considered. We also emphasize the concrete and useful expression of algorithms in the form of computer software.
