The NATO Advanced Study Institute on "Computer algorithms for solving linear algebraic equations: the state of the art" was held September 9-21, 1990, at II Ciocco, Barga, Italy. It was attended by 68 students (among them many well known specialists in related fields!) from the following countries: Belgium, Brazil, Canada, Czechoslovakia, Denmark, France, Germany, Greece, Holland, Hungary, Italy, Portugal, Spain, Turkey, UK, USA, USSR, Yugoslavia. Solving linear equations is a fundamental task in most of computational mathematics. Linear systems which are now encountered in practice may be of very large dimension and their solution can still be a challenge in terms of the requirements of accuracy or reasonable computational time. With the advent of supercomputers with vector and parallel features, algorithms which were previously formulated in a framework of sequential operations often need a completely new formulation, and algorithms that were not recommended in a sequential framework may become the best choice. The aim of the ASI was to present the state of the art in this field. While not all important aspects could be covered (for instance there is no presentation of methods using interval arithmetic or symbolic computation), we believe that most important topics were considered, many of them by leading specialists who have contributed substantially to the developments in these fields.

Inhalt

1. Classical Methods for Linear Equations.- 2. Complexity of Algorithms for Linear Systems of Equations.- 3. Algorithms for Linear Least Squares Problems.- 4. ABS Algorithms for General Linear Systems.- 5. ABS Algorithms for Sparse Linear Systems.- 6. Multi-Grid Algorithms. Introduction, Survey and Convergence Analysis.- 7. Two Multi-Level Methods for Nonuniformly Refined Grids.- 8. Preconditioning Methods for Block H-Matrices.- 9. Domain Decomposition Methods for Solving Large Sparse Linear Systems.- 10. A Splitting Method for Large Sparse Linear Systems on a Multivector Computer.- 11. Scheduling Parallel Factorization Algorithms on a Shared Memory Computer.- 12. Gaussian Elimination on Distributed Memory Architectures.- 13. Parallel Algorithms for General Sparse Systems.- 14. The Solution of Partially Separable Linear Equations on Parallel Processing Systems.- Author Index.- List of Participants.