Numerical Solution of Eigenvalue Problems and Related Least Squares Problems

特征值问题及相关最小二乘问题的数值解

• 批准号: 9424435
• 负责人: Jesse Barlow
• 金额: $ 14.96万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-08-01 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9424435&HistoricalAwards=false
• 关键词: Numerical; Solution; Eigenvalue; Problems; Related

This research seeks to improve the accuracy of methods to solve some particular eigenvalue problems. The first is the classical symmetric eigenvalue problem. Recent results have shown that there is a large class of symmetric eigenvalue problems for which small structured perturbations result in small changes in the eigenvalues in the relative sense. This class of matrices is called ``well-behaved''. The problem of finding a necessary and sufficient condition for a matrix to be ``well-behaved'' is being investigated. A number of related issues have to be considered, including: analysis of methods for updating indefinite eigenvalue problems; investigation of methods for updating the ULV and ULLV approximations to the singular value decomposition and generalized singular value decomposition; and development of analysis of methods for computing the sparse generalized singular value decomposition. The last two issues are extremely important in the solution of ill-posed least squares problems and total least squares problems. The implications of derived results for these problems are being investigated.

本研究的目的是提高方法的精度，以解决一些特殊的特征值问题。 的 首先是经典的对称特征值问题。 最近的结果 证明了存在一大类对称特征值问题， 小的结构性扰动导致特征值的小变化， 相对意义。 这类矩阵被称为“良序矩阵”。 的 寻找矩阵成立的充分必要条件的问题 “好”正在调查中。 一些相关的问题必须 考虑，包括：更新不定特征值问题的方法分析;调查的方法， 将ULV和ULLV近似更新为奇异 值分解与广义奇异值 分解;和发展分析的方法计算稀疏广义奇异值 分解 最后两个问题在解决 不适定最小二乘问题和总体最小二乘问题。 的影响 这些问题的衍生结果正在研究中。