"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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=593951
• 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.

数值线性代数是大多数科学计算的核心。许多科学、工程和其他问题都可以在计算机上最有效地表示和解决，例如矩阵问题或线性代数问题。数值线性代数的重要应用领域之一是估计。本研究旨在开发数值可靠且高效的算法和软件，用于解决通信、信号处理、全球导航卫星系统和统计等实际领域中可能出现的一般和特定估计问题。这些问题可以是小规模的，也可以是大规模的规模。本研究还对算法进行了分析，以显示其可靠性，并对问题进行了敏感性分析，以显示数据变化引起的有限精度计算或数据的不确定性会对最终结果产生什么影响。