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.

这个由纽约大学科朗研究所的Anne Greenbaum和捷克科学院计算机与信息科学研究所的Zdenek Strakos合作的美国-捷克研究项目的主要目标是分析和开发迭代方法，用于解决在许多科学计算领域出现的非对称线性系统和特征值问题。目前解决这类问题的迭代方法有时是有效的，但缺乏坚实的理论基础，可能不够健壮。格林鲍姆博士和斯特拉科斯博士打算制定确定迭代方法有效性的标准，并设计满足这些标准的新方法。他们将分析满足这些标准的克里洛夫空间方法。他们将分析Krylov空间方法，并考虑从不同空间选择近似的优点。研究人员希望解释双共轭梯度和准最小残差（QMR）方法的成功，并分析有限精度算法对这些算法的影响。他们还将研究各种算法的并行性潜力，并为特定的机器架构开发并行实现。总的结果有望有助于我们解决大型稀疏线性方程的能力。这类问题的迭代算法是科学和工程中众多计算求解方法的关键。这个计算数学项目通过使美国和捷克斯洛伐克的顶尖专家在共同感兴趣和能力强的领域结合互补的人才和汇集研究资源，实现了推进科学的计划目标。