A PhD thesis @ NALAG
This is a PhD thesis prepared by a member of the NALAG group or prepared with a (co)promotor from NALAG.
TW 2015_04
Ben Jeuris Advisor(s): Raf Vandebril and Johannes Nicaise Abstract Optimization is an area of research that finds applications in almost every domain. As an example we consider the matrix geometric mean. For real numbers, this mean is simply the nthnbsp;of the product of the n numbers. Matrices, however, fail to have such a simple expression for the mean sincenbsp;do not commute (i.e. the product AB is not necessarily equal to the product BA). To overcome this issue we consider the matrices as living on a curved surface. We will computenbsp;matrix mean by solving an optimization problem on this surface. We then attempt to generalize traditional optimization techniques, taking into account the additional difficulties that arise on these curved surfaces coming from particular matrix structures. An important aspect of the PhD is to exploit the maximum of structure of the matrix spaces at hand, and to develop techniques to deal with gaps in the curved surface. Doctadmin 3E110513 / lirias 496544 / mailto: nalag team< |