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.

研究人员将研究用于解决中度至大规模特征值和广义特征值问题的数值算法。有两条研究。一种是研究一种新型可行的Hessenberg特征值算法，称为“划分驱动”。 驱动算法的细分算法降低了计算复杂性，并增加了Hessenberg特征值问题的并行性。这有可能降低Hessenberg特征值问题的计算成本显着低于当前水平。其他研究线涉及持续开发TTQRE，TTQRE是一种用于解决中等规模代数特征值问题的变体QR算法。尽管TTQRE已经证明自己是传统QR算法的重大进步，但尚未发挥其全部潜力。将设计策略，以在执行过程中动态调整其基本参数。该项目支持将参加该项目的研究生。学生的培训将受益于实际平行计算机上的实用计算经验，从理论问题的工作中受益。