Print Email Facebook Twitter Hierarchically semi-separable representation and its applications Title Hierarchically semi-separable representation and its applications Author Sheng, Z. Contributor Dewilde, P. (mentor) van der Veen, A.J. (mentor) van der Meijs, N. (mentor) Remis, R.F. (mentor) Faculty Electrical Engineering, Mathematics and Computer Science Date 2006-06-01 Abstract In this thesis, we study a important class of structured matrices: "Hierarchically Semi-Separable" matrices, for which an efficient hierarchically state based representation called Hierarchically Semi- Separable (HSS) representation can be used to represent it with a small amount of parameters that are linear in the dimension of the matrix. Under the framework of this HSS representation, efficient matrix transformation algorithms that are linear in the number of equations are given. In particular, a system Ax = b can be solved with linear complexity. Also, LU and URV factorization can be efficiently executed. There is a close connection between HSS matrices and classical Semi Separable matrices (sometimes called Sequentially Semi Separable matrices or SSS matrices or equivalently, time-varying systems), and a number of results of SSS theory can be translated to parallel results in the HSS theory (neither class contains the other however). We also discuss the limitation of the direct HSS algorithms, for which iterative solution algorithms based on HSS representation and its basic algorithms should come to rescue. A number of preconditioner construction algorithms based on HSS representation have been proposed. Subject hierarchically semi-separable matrixlinear solverpreconditionerluurv factorization To reference this document use: http://resolver.tudelft.nl/uuid:e7a452de-6859-42bc-97b6-3eb28815dc8b Publisher TU Delft, Electrical Engineering, Mathematics and Computer Science, Information and Communication Technology (ICT) Part of collection Student theses Document type master thesis Rights (c) 2006 Z. Sheng Files PDF ewi_sheng_2006.pdf 2.31 MB Close viewer /islandora/object/uuid:e7a452de-6859-42bc-97b6-3eb28815dc8b/datastream/OBJ/view