Eigensystem Computations

特征系统计算

• 批准号: 8800437
• 负责人: David Watkins
• 金额: --
• 依托单位: Washington State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8800437&HistoricalAwards=false
• 关键词: Eigensystem; Computations

This project is concerned with the development of algorithms for calculating the eigensystems of general matrices by reducing them to a form which is more compact than the usual Hessenberg form and by applying the LR algorithm ot the condensed form. Preliminary tests suggest that the proposed algorithm will produce accurate results in a much shorter time than the standard QR algorithm for a dense eigensystem. For the most condensed form of a tridiagonal matrix, a divide-and-conquer algorithm will be developed for use in parallel computers. For a specialized Hamilton eigenvalue problem which requires the solution of an algebraic Riccati equation, our algorithm will be based on symplectic similarity transformations which preserve the Hamiltonian structure of the matrix.

该项目涉及开发用于计算一般矩阵的特征系统的算法，通过将其简化为比通常的Hessenberg形式更紧凑的形式，并通过应用凝结形式的LR算法。初步测试表明，所提出的算法将在密集特征系统的标准QR算法短得多的时间内产生准确的结果。对于最凝结的三角基矩阵形式，将开发出一种用于并行计算机中的分裂和诱导算法。对于需要解决代数riccati方程解决方案解决方案的专业汉密尔顿特征值问题，我们的算法将基于保持矩阵的汉密尔顿结构的象征性相似性变换。