U.S.-Germany Cooperative Research in Applied and Computational Mathematics: Analysis of Block and Two-Stage Iterative Methods

该奖项支持教授丹尼尔Szyld的 坦普尔大学将在应用和 计算数学与教授安德烈亚斯 应用数学研究所的Frommer 卡尔斯鲁厄大学，德国。 的 两名研究人员从不同的角度 的迭代方法的研究 线性和非线性有效解 代数方程组 串行和并行计算机。 Frommer已经 广泛研究线性和非线性 异步方法和多分裂 方法. Szyld和他的合著者致力于 两阶段方法，包括所需工具 他们的分析和计算 实验 最近，两位合作者 完成了两阶段迭代法的研究 H矩阵 在新的工作中，他们 将把这项研究扩展到两个阶段 方法和异步（混沌）并行 方法. 他们将研究两种融合 属性以及实现细节。 这项工作在很大程度上依赖于补充 每个人都在以前的工作中发展的专业知识。 在许多科学和 工程应用是解决 大型线性代数方程组。 合作的科学家们将研究 理论的、计算的和算法的 这些系统的解决方案的各个方面， 他们的应用。 建设项目可能 导致标准，以确定最佳或 近似最优的内部迭代次数， 保证整体收敛， 并行计算时间

This award supports Professor Daniel Szyld of Temple University to collaborate in applied and computational mathematics with Professor Andreas Frommer of the Institute for Applied Mathematics of the University of Karlsruhe, Germany. The two researchers have worked on different aspects of the study of iterative methods for the efficient solution of linear and nonlinear algebraic systems of equations on both sequential and parallel computers. Frommer has worked extensively on linear and nonlinear asynchronous methods and on multisplitting methods. Szyld and his coauthors have worked on two-stage methods, including the tools needed for their analysis and computational experiments. Recently the two collaborators completed a study of two-stage iterative methods for H-matrices. In the proposed new work, they will extend this study to block two-stage methods and asynchronous (chaotic) parallel methods. They will look at both convergence properties as well as implementation details. This work relies heavily on the complementary expertise that each has developed in prior work. A central problem in many science and engineering applications is the solution of large linear systems of algebraic equations. The cooperating scientists will study theoretical, computational and algorithmic aspects of the solution of such systems and their applications. The project is likely to result in criteria to determine an optimal or near-optimal number of inner iterations to guarantee overall convergence and reduce parallel computing time.