U.S.-Czechoslovakia Mathematics Research on Iterative Methods for Nonsymmetric Linear Systems and Eigenvalue Problems

美国的主要目标是-捷克研究项目， 纽约大学柯朗研究所的安妮·格林鲍姆和 Zdenek Strakos，计算机和信息研究所 科学，捷克科学院，是分析和发展 迭代法求解非对称线性方程组， 在许多科学领域中出现的特征值问题 计算的 当前求解此类问题的迭代方法 有时有效，但缺乏坚实的理论基础， 可能不是鲁棒的。 格林鲍姆博士和斯特拉科斯博士打算 制定标准，以确定迭代的有效性 方法，并设计新的方法，这些标准将 满意 他们将分析Krylov空间方法， 标准将得到满足。 他们将分析Krylov空间方法 并考虑选择近似值的优点， 空间也不同。 研究人员希望解释 双共轭梯度和QMR（准最小）的成功 残差）方法，并分析有限精度的影响 在这些算法上进行运算。 他们还将研究 在各种算法的并行性和开发并行 具体机器架构的实现。 完全 结果预计将有助于我们解决大型稀疏 线性方程 这类问题的迭代算法是 科学中的许多计算解决方案， 工程. 这个计算数学项目实现了这个程序， 通过让领先的专家参与进来来推进科学的目标 美国和捷克斯洛伐克将联合收割机互补的人才和 在共同感兴趣的领域集中研究资源， 能力。

The primary objective of this U.S.-Czech research project between Anne Greenbaum of the New York University Courant Institute and Zdenek Strakos of the Institute of Computer and Informations Science, Czech Academy of Sciences, is to analyze and develop iterative methods for solving the non-symmetric linear systems and eigenvalue problems that arise in many areas of scientific computing. Current iterative methods for solving such problems are sometimes effective but lack a firm theoretical foundation and may not be robust. Dr. Greenbaum and Dr. Strakos intend to develop criteria for determining the effectiveness of an iterative method and to design new methods for which these criteria will be satisfied. They will analyze Krylov space methods for shich these criteria will be satisfied. They will analyze Krylov space methods and consider the advantages of choosing approximations from different spaces as well. The researchers hope to explain the success of the biconjugate gradient and QMR (Quasi-Minimal Residual) methods and to analyze the effects of finite precision arithmetic on these algorithms. They also will study the potential for parallelism in various algorithms and develop parallel implementations for specific machine architectures. Altogether results are expected to contribute to our ability to solve large sparse linear equations. Iterative algorithms for such problems are keys to numerous computational solution methods in science and engineering. This project in computational mathematics fulfills the program objectives of advancing science by enabling leading experts in the U.S. and Czechoslovakia to combine complementary talents and pool research resources in the areas of strong mutual interest and competence.