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、工程和其他问题都可以在计算机上最有效地表示并解决，例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。本研究还进行了分析的算法，以显示其可靠性和敏感性分析的问题，以显示在数据中的有限精度的计算或数据的不确定性所造成的变化将对最终结果的影响。

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.