Řešení soustav lineárních rovnic s obroubenou maticí
Solving bordered linear systems
diplomová práce (OBHÁJENO)
Zobrazit/ otevřít
Trvalý odkaz
http://hdl.handle.net/20.500.11956/9357Identifikátory
SIS: 43070
Kolekce
- Kvalifikační práce [11199]
Autor
Vedoucí práce
Oponent práce
Zítko, Jan
Fakulta / součást
Matematicko-fyzikální fakulta
Obor
Výpočtová matematika
Katedra / ústav / klinika
Katedra numerické matematiky
Datum obhajoby
29. 5. 2007
Nakladatel
Univerzita Karlova, Matematicko-fyzikální fakultaJazyk
Čeština
Známka
Výborně
The comparison of two algorithms for solving bordered linear systems is considered. The matrix of this system consists of four blocks (matrices A,B,C,D), the upper left one is a sparse matrix A, which is ill-conditioned and structured. The other blocks (B,C,D) are dense. We say that the matrix A is bordered with the matrices B,C,D. It is desirable to preserve the block structure of the matrix and take advantage of sparsity and structure of the matrix A. The literature suggests to use two different algorithms: The first one is the method BEM for matrices with the borders of width equal to one. The recursive alternative for matrices with wider borders is called BEMW. The second algorithm is an iterative method. Both techniques are based on different variants of the block LU-decomposition.