Preconditioning Techniques for Large Linear Systems: A Survey

Preconditioning Techniques for Large LinearSystems: A Survey

This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions. Some of the challenges ahead are also discussed. An e...

Some Preconditioning Techniques for Linear Systems

New convergence intervals of parameters αi are derived and applied for solving the modified linear systems, which enables a better understanding of how parameters should be chosen. The convergence theorem for H-matrix is given. Meanwhile, we discuss the convergence results forM -matrices linear systems and give some new preconditioners. Numerical examples are used to illustrate our results. Key...

Preconditioning Techniques for Sparse Linear Systems

Enhanced Parallel Multicolor Preconditioning Techniques for Linear Systems

When solving a linear system in parallel, a large overhead in using an incomplete LU factorization as a preconditioner may annihilate any gains made from the improved convergence. This overhead is due to the inherently sequential nature of such a preconditioning. Multicoloring of the subdomains assigned to processors is a common remedy for increasing the parallelism of a global ordering. Howeve...

Symbolic preconditioning techniques for linear systems of partial differential equations

Some algorithmic aspects of systems of PDEs based simulations can be better clarified by means of symbolic computation techniques. This is very important since numerical simulations heavily rely on solving systems of PDEs. For the large-scale problems we deal with in today’s standard applications, it is necessary to rely on iterative Krylov methods that are scalable (i.e., weakly dependent on t...