Iterative Methods and Matrix Analysis (Computer Science)

迭代方法和矩阵分析（计算机科学）

• 批准号: 9450191
• 负责人: Anne Greenbaum
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-09-01 至 1995-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9450191&HistoricalAwards=false
• 关键词: Iterative; Methods; Matrix; Analysis; Computer

This research is aimed at analyzing and developing iterative methods for solving the nonsymmetric linear systems that arise in many areas of scientific computing. Current iterative methods for solving such problems ar sometimes effective but lack a firm theoretical foundation and may not be robust. Krylov space methods, such as GMRES, will be analyzed and the idea of choosing approximations from different spaces will also be considered. The biconjugate gradient and QMR algorithms will be related and an attempt made to explain their success. Potential for parallelism in various algorithms will be studied and parallel implementations will be developed for specific machine architectures. Collaborations are planned with Nick Trefethen and others in the Computer Science Department at Cornell. Two main activities for interacting with students are: teaching a graduate seminar ("CS 722") on iterative methods and matrix analysis, to familiarize students and other interested scientists and the state of the art in this field; and introducing a sophomore level practicum where, in conjunction with the numerical analysis course CS 222, students will implement parallel numerical algorithms on the machines available at the Cornell Theory Center. Various undergraduate seminars will be organized related to this activity.

这项研究的目的是分析和开发求解科学计算中许多领域中出现的非对称线性方程组的迭代方法。目前解决此类问题的迭代方法有时是有效的，但缺乏坚实的理论基础，而且可能不是很健壮。将分析Krylov空间方法，如GMRES，并将考虑从不同空间选择近似的想法。双共轭梯度算法和QMR算法将相互关联，并试图解释它们的成功。将研究各种算法中并行性的可能性，并针对特定的机器体系结构开发并行实现。计划与尼克·特雷费森和康奈尔大学计算机科学系的其他人合作。与学生互动的两个主要活动是：教授关于迭代方法和矩阵分析的研究生研讨会(“CS 722”)，以熟悉学生和其他感兴趣的科学家以及该领域的最新技术；以及引入二年级水平的实践，结合数值分析课程CS 222，学生将在康奈尔理论中心提供的机器上实施并行数值算法。将组织各种与此活动相关的本科生研讨会。