A Combinatorial Scheme for Developing Efficient Composite Solvers
A Combinatorial Scheme for Developing Efficient Composite Solvers
复制标题
开发高效复合求解器的组合方案
DOI：
10.1007/3-540-46080-2_34
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
K. Teranishi
中科院分区：
文献类型：
--
作者：
S. Bhowmick;P. Raghavan;K. Teranishi
科学计算中的许多基本问题都有不止一种求解方法。替代解决方案方法在解决方案成本和可靠性之间进行不同的权衡并不罕见。此外，求解方法的性能通常取决于问题实例的数值属性，因此在不同的应用领域中可能会有很大的差异。在这种情况下，自然会考虑构建多方法复合求解器，以潜在地提高平均性能和可靠性。在本文中，我们提供了一个组合框架，开发这样的复合求解器。我们提供的分析结果，从一组方法与性能和可靠性的归一化措施获得最佳的复合材料。我们的实证结果表明，这种最佳的复合材料解决大型，稀疏的线性方程组的有效性。
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.