Algorithms, analysis and applications of numerical linear algebra

数值线性代数是大多数科学计算的核心。许多科学、工程和其他问题都以矩阵问题或线性代数问题的形式在计算机上得到最有效的表示和解决。数值线性代数的一个重要应用领域是估计。本研究旨在开发数值上可靠且高效的算法和软件，以解决在通信、信号处理、全球卫星导航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。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引起的数据变化或数据的不确定性对最终结果的影响。这项研究的结果不仅对科学计算的研究有价值，而且对工业，特别是对通信技术公司和GNSS接收器制造商有价值。

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 by 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 scientific computing but also to industry, particularly to the communications technology companies and GNSS receiver manufactures.