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.