"Algorithms, Analysis, Applications and Software of Numerical Linear Algebra"

《数值线性代数的算法、分析、应用和软件》

• 批准号: 217191-2012
• 负责人: Chang, XiaoWen
• 金额: $ 1.6万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=570114
• 关键词: Algorithms; Analysis; Applications; Software; Numerical

Numerical linear algebra is at the core of most scientific computing. Many scientific, engineering, and other problems are most effectively represented and then solved on computers, as matrix problems, or linear algebra problems. One of the important applied areas of numerical linear algebra is estimation. This research aims to develop numerically reliable and efficient algorithms and software for solving general and specific estimation problems which may arise in practical areas such as communications, signal processing, global navigation satellite systems, and statistics etc. These problems can be either small scale or large scale. This research also carries out the analyses of the algorithms to show their reliability and sensitivity analyses of the problems to show what effects changes in data caused finite precision computation or uncertainty in the data will have on the final results. The outcome of this research will be valuable not only to the study of numerical linear algebra but also to industry, particularly to the communications technology companies and manufactures of global navigation satellite systems receivers.

数值线性代数是大多数科学计算的核心。许多科学、工程和其他问题在计算机上最有效地表示和解决，如矩阵问题或线性代数问题。数值线性代数的一个重要应用领域是估计。本研究的目的是开发数值可靠和有效的算法和软件，用于解决一般和特定的估计问题，可能会出现在实际领域，如通信，信号处理，全球导航卫星系统，统计等，这些问题可以是小规模或大规模。本研究还对算法进行了分析，以显示其可靠性和问题的敏感性分析，以显示有限精度计算或数据不确定性引起的数据变化对最终结果的影响。 本研究的成果不仅对数值线性代数的研究有价值，而且对工业界，特别是对通信技术公司和全球导航卫星系统接收器制造商也有价值。