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

美捷数学非对称线性系统与特征值问题迭代方法研究

• 批准号: 9218024
• 负责人: Anne Greenbaum
• 金额: $ 1.01万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9218024&HistoricalAwards=false
• 关键词: U.S.; Czechoslovakia; Mathematics; Research; Iterative

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.

捷克科学院纽约大学库兰特学院的安妮·格林鲍姆（Anne Greenbaum）与计算机和信息科学研究所的ZDENEK Strakos之间的美国捷克研究项目的主要目标是分析和开发迭代方法，以解决非对称的方法线性系统和特征值问题在科学计算的许多领域都会出现。 当前解决此类问题的迭代方法有时是有效的，但缺乏坚定的理论基础，可能并不强大。 Greenbaum博士和Strakos博士打算制定标准来确定迭代方法的有效性，并设计将满足这些标准的新方法。 他们将分析Krylov空间方法的这些标准。 他们将分析Krylov空间方法，并考虑从不同空间选择近似值的优势。 研究人员希望解释双轭梯度和QMR（准最小残留）方法的成功，并分析有限精确算术对这些算法的影响。 他们还将研究各种算法中并行性的潜力，并为特定的机器架构开发并行实现。 总共有望有助于我们解决大型稀疏线性方程的能力。 有关此类问题的迭代算法是科学和工程中众多计算解决方案方法的关键。 该计算数学项目实现了通过使美国和捷克斯洛伐克的领先专家在强大的共同利益和能力领域中结合互补才能和汇总研究资源来实现进步科学的计划。