Итерационные методы решения систем линейных уравнений, от прошлого к будущему

The numerical simulation of many technical and scientific problems leads to the solution of extremely large and sparse linear systems. Advanced computer architectures - vector and parallel computers – and state-of-the-art algorithms have to be used in order to solve these systems with a sufficient accuracy in a reasonable time. Importantly, the simulation of many problems is only possible by the combination of technical and algorithmic progress.
Classical solvers for symmetric and positive definite matrices will be reviewed. From this starting point it will be shown that modern solvers rely on the same principles. With this knowlege the methods can be easily classified despite of their confusing variety. Morever, it will be shown how to parallelize modern solvers. Thus, the efficient use of advanced computer architectures is combined with modern algorithms to achieve a high perfomance.