Title: | Modified Gaussian Elimination without Division Operations |
Authors: | Skala, Václav |
Citation: | AIP Conference Proceedings, p. 1936-1939. |
Issue Date: | 2013 |
Publisher: | American Institute of Physics |
Document type: | preprint preprint |
URI: | http://dx.doi.org/10.1063/1.4825912 http://hdl.handle.net/11025/11735 |
ISBN: | 978-0-7354-1184-5 |
ISSN: | 0094-243X |
Keywords: | lineární algebra;parciální diferenciální rovnice;Gaussian elimination;numerické metody |
Keywords in different language: | linear algebra;partial differential equations;Gaussova eliminace;numerical methods |
Abstract: | A new modified method based on the Gaussian elimination method for solution of linear system of equations in the projective space is formulated. It is based on application of projective extension of the Euclidean space and use of homogeneous coordinates. It leads to an elimination of division operation and higher precision due to division operation elimination. The approach is based on understanding that a solution of the linear system is equivalent to the extended cross-product, i.e. . As it can be seen there no division is needed. Use of the projective representation enables to avoid division operation and use advantages of the matrix-vector architectures. Division operations have to be used only if the final result of computation has to be in the Euclidean representation. The proposed method was implemented in C# and C++ and experimentally verified. It is especially convenient for computations on GPUs based architectures. |
Rights: | Original article published under © 2013 AIP Publishing LLC |
Appears in Collections: | Preprinty / Preprints (KIV) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
2013_ICNAAM-Gauss_Elimination.pdf | Plný text | 956,45 kB | Adobe PDF | View/Open |
Please use this identifier to cite or link to this item:
http://hdl.handle.net/11025/11735
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.