Algorithmic bombardment for the iterative solution of linear systems: a poly-iterative approach
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
Matrix computations (3rd ed.)
Developing Component Architectures for Distributed Scientific Problem Solving
IEEE Computational Science & Engineering
Faster PDE-based simulations using robust composite linear solvers
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Adaptive Software for Scientific Computing: Co-Managing Quality-Performance-Power Tradeoffs
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 10 - Volume 11
Autotuning multigrid with PetaBricks
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
The role of multi-method linear solvers in PDE-based simulations
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
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Many fundamental problems in scientific computing have more than one solution method. It is not uncommon for alternative solution methods to represent different tradeoffs between solution cost and reliability. Furthermore, the performance of a solution method often depends on the numerical properties of the problem instance and thus can vary dramatically across application domains. In such situations, it is natural to consider the construction of a multi-method composite solver to potentially improve both the average performance and reliability. In this paper, we provide a combinatorial framework for developing such composite solvers. We provide analytical results for obtaining an optimal composite from a set of methods with normalized measures of performance and reliability. Our empirical results demonstrate the effectiveness of such optimal composites for solving large, sparse linear systems of equations.