Hierarchically semi-separable representation and its applications

  • Sheng, Z. (author)
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Publication date
June 2006
Publisher
TU Delft, Electrical Engineering, Mathematics and Computer Science, Information and Communication Technology (ICT)

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 ...

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