Computations of Nonsymmetric Eigenvalue Problems and the Generalized Singular Value Decomposition

非对称特征值问题的计算和广义奇异值分解

• 批准号: 9102963
• 负责人: Zhaojun Bai
• 金额: $ 4.22万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-15 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102963&HistoricalAwards=false
• 关键词: Computations; Nonsymmetric; Eigenvalue; Problems; Generalized

With the availability of advanced computing facilities and the improvement of the environment of floating point arithmetic, there is a need and an opportunity for further development and analysis of accurate, stable and efficient numerical solutions for many numerical linear algebra problems. This proposal is concerned with several fundamental matrix computation problems, such as computing eigenvalues of large nonsymmetric matrices, computing invariant subspaces with specific spectra, estimating condition numbers of the nonsymmetric eigenvalue problem, and computing the generalized QR factorization and the generalized singular value decomposition. The goal of the research is to develop efficient algorithms and portable software for high- performance computers, motivated by many applications of these problems in scientific computing and other areas of numerical analysis.

随着先进计算设施的出现和浮点运算环境的改善，有必要也有机会进一步开发和分析许多数值线性代数问题的精确、稳定和高效的数值解。 该提案涉及几个基本的矩阵计算问题，例如计算大型非对称矩阵的特征值、计算具有特定谱的不变子空间、估计非对称特征值问题的条件数以及计算广义 QR 分解和广义奇异值分解。 该研究的目标是为高性能计算机开发高效的算法和便携式软件，其动机是这些问题在科学计算和其他数值分析领域的许多应用。