Název: Modified Gaussian Elimination without Division Operations
Autoři: Skala, Václav
Citace zdrojového dokumentu: AIP Conference Proceedings, p. 1936-1939.
Datum vydání: 2013
Nakladatel: American Institute of Physics
Typ dokumentu: 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
Klíčová slova: lineární algebra;parciální diferenciální rovnice;Gaussian elimination;numerické metody
Klíčová slova v dalším jazyce: linear algebra;partial differential equations;Gaussova eliminace;numerical methods
Abstrakt: 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.
Práva: Original article published under © 2013 AIP Publishing LLC
Vyskytuje se v kolekcích:Preprinty / Preprints (KIV)

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