Algorithms, analysis and applications of numerical linear algebra

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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.