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Analysis and Improvement of Linear and Nonlinear Eigenvalue Algorithms Based on Geometric Approaches

Analysis and Improvement of Linear and Nonlinear Eigenvalue Algorithms Based on Geometric Approaches
基于几何方法的线性和非线性特征值算法的分析与改进
批准号：
9971591
负责人：
Alan Edelman
金额：
$15.0万
依托单位：
Massachusetts Institute of Technology
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1999
资助国家：
美国
项目状态：
已结题
起止时间：
1999-07-15 至 2003-06-30
来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971591&HistoricalAwards=false
关键词：
AnalysisImprovementLinearNonlinearEigenvalue

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中文摘要
翻译
主要研究人员建议继续与学生一起研究计算数学，从数学概念到实用的数值软件。目标是进一步应用现代几何方法来开发和理解与特征值例程有关的算法的精度和故障，以及在存在正交性约束的数值优化中。我们所研究的各种数值软件在许多科学和工程领域都有广泛的应用。这些算法常常工作得很好，但众所周知，有时也会失败；新的复杂分析被提出来解决这些问题。在教育方面，这些算法将用于课堂设置。
英文摘要
ABSTRACT The principal investigator proposes to continue his work with students on computationalmathematics from mathematical conception to useful numerical software.The objectives are the furtherapplication of modern geometrical methods towards the development and understanding of accuracy and failures of algorithms related toeigenvalue routines and in numerical optimization in the presenceof orthogonality constraints. The kinds of numerical software that we investigatemathematically are widely used in many scientificand engineering fields. These algorithms oftenwork very well, but are also known to fail onoccasion; new sophisticated analyses are proposedto fix these problems. On the education side,these algorithms will be used in classroom settings.
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