Block Overrelaxation Methods For Indefinite Least Squares Problems

The least squares problem is one of the most important and widely usedtools in many fields, such as economics, statistics, optimization, engineering,automation, etc, which has attracted many numerical algebra analysts toinvestigate the numerical stabilities of the least squares problem. This papermainly studies two kinds of block splitting iterative methods for the indefiniteleast squares (ILS) problem, and also gives the convergence regions and theoptimal parameters. We briefly introduce our work as follows.In this thesis, we first introduce the splitting iterative methods for linearsystems. By reducing the ILS problem into the augmented KKT form andapplying the block splitting iterative methods on the augmented system, the ILSproblem can be solved.We then investigate the process of using the2-block symmetric successiveoverrelaxation (SSOR) and2-block accelerated overrelaxation (AOR) methodsfor the solution of ILS problem. The convergence regions and the optimalparameters of these two methods are also given. We conclude that the optimalAOR converges faster than the optimal SSOR, but the latter one has a verysimple optimal parameter.Finally, several numerical examples are presented to illustrate the resultsand a comparison is included.