Numerical Linear Algebra and Eigenvalue Computations

数值线性代数和特征值计算

• 批准号: 0098150
• 负责人: Ralph Byers
• 金额: $ 20.25万
• 依托单位: University of Kansas Center for Research Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0098150&HistoricalAwards=false
• 关键词: Numerical; Linear; Algebra; Eigenvalue; Computations

The investigator will study numerical algorithms for solving moderate to large scale eigenvalue and generalized eigenvalue problems. There are two lines of research. One is to investigate a new kind of parallelizable Hessenberg eigen-value algorithm termed "subdivision-by-deflation". The subdivision-by-deflation algorithm reduces the computational complexity and increases the parallelism of Hessenberg eigenvalue problems. This has the potential of reducing the computational cost of the Hessenberg eigenvalue problem significantly below current levels.The other line of research involves continued development of TTQRE, a variant QR algorithm for solving the moderate scale algebraic eigenvalue problem. Although TTQRE has already proved itself to be a significant advance over traditional QR algorithms, it has not yet reached its full potential. Strategies will be designed that adjust its fundamental parameters dynamically during execution. This project supports a graduate student who will participate in the project. The student's training will benefit from practical computational experience on real parallel computers as from the work with theoretical problems.

研究人员将研究求解中、大规模特征值问题和广义特征值问题的数值算法。有两条研究路线。一种是研究一种新的可并行化的Hessenberg特征值算法，称为“按收缩细分”。该算法降低了Hessenberg特征值问题的计算复杂度，提高了并行度。这有可能将Hessenberg特征值问题的计算量大大降低到当前水平以下。另一项研究涉及继续开发TTQRE，这是一种求解中等尺度代数特征值问题的变种QR算法。尽管TTQRE已经被证明是对传统QR算法的重大进步，但它还没有充分发挥其潜力。将设计在执行过程中动态调整其基本参数的策略。该项目支持一名将参与该项目的研究生。学生的训练将受益于在实际并行计算机上的实际计算经验，以及理论问题的工作。