Helpdesk

Top image

Editorial board

Juraj Altus
University of Zilina, Slovakia

Alexander Argyros
The University of Sydney, Australia

Radu Arsinte
Technical University of Cluj Napoca, Romania

Ivan Baronak
Slovak University of Technology, Slovakia

Dalibor Biolek
University of Defence, Czech Republic

Klara Capova
University of Zilina, Slovakia

Ray-Guang Cheng
National Taiwan University of Science and Technology, Taiwan, Province of China

Erik Chromy
UPC Broadband Slovakia, Slovakia

Frantisek Cvachovec
University of Defence, Czech Republic

Annraoi M de Paor
University College Dublin, Ireland

Milan Dado
University of Zilina, Slovakia

Zdenek Divis
VSB - Technical University of Ostrava, Czech Republic

Petr Drexler
Brno University of Technology, Czech Republic

Pavel Fiala
Brno University of Technology, Czech Republic

Eva Gescheidtova
Brno University of Technology, Czech Republic

Valeria Hrabovcova
University of Zilina, Slovakia

Gokhan Hakki Ilk
Ankara University, Turkey

Rene Kalus
VSB - Technical University of Ostrava, Czech Republic

Ivan Kasik
Academy of Sciences of the Czech Republic, Czech Republic

Vladimir Kasik
VSB - Technical University of Ostrava, Czech Republic

Jan Kohout
University of Defence, Czech Republic

Pavel Koktavy
Brno University of Technology, Czech Republic

Ondrej Krejcar
University of Hradec Kralove, Czech Republic

Igor Piotr Kurytnik
University of Bielsko-Biala, Poland

Miroslaw Luft
Technical University of Radom, Poland

Stanislav Marchevsky
Technical University of Kosice, Slovakia

Luigi Martirano
University of Rome "La Sapienza", Italy

Jerzy Mikulski
University of Economics in Katowice, Katowice, Poland

Karol Molnar
Honeywell International, Czech Republic

Miloslav Ohlidal
Brno University of Technology, Czech Republic

Ibrahim Taner Okumus
Sutcu Imam University, Turkey

Milos Orgon
Slovak University of Technology, Slovakia

Marek Penhaker
VSB - Technical University of Ostrava, Czech Republic

Wasiu Oyewole Popoola
The University of Edinburgh, United Kingdom

Roman Prokop
Tomas Bata University in Zlin, Czech Republic

Karol Rastocny
University of Zilina, Slovakia

Marie Richterova
University of Defence, Czech Republic

Gheorghe Sebestyen-Pal
Technical University of Cluj Napoca, Romania

Sergey Vladimirovich Serebriannikov
National Research University "MPEI", Russian Federation

Yuriy Shmaliy
Guanajuato University, Mexico

Vladimir Schejbal
University of Pardubice, Czech Republic

Bohumil Skala
University of West Bohemia in Plzen, Czech Republic

Lorand Szabo
Technical University of Cluj Napoca, Romania

Adam Szelag
Warsaw University of Technology, Poland

Ahmadreza Tabesh
Isfahan University of Technology, Iran, Islamic Republic Of

Mauro Tropea
DIMES Department of University of Calabria, Italy

Pavel Vaclavek
Brno University of Technology, Czech Republic

Martin Vaculik
University of Zilina, Slovakia

Viktor Valouch
Academy of Sciences of the Czech Republic, Czech Republic

Vladimir Vasinek
VSB - Technical University of Ostrava, Czech Republic

Jiri Vodrazka
Czech Technical University in Prague, Czech Republic

Miroslav Voznak
VSB - Technical University of Ostrava, Czech Republic

Otakar Wilfert
Brno University of Technology, Czech Republic

Jan Zidek
VSB - Technical University of Ostrava, Czech Republic


Home Search Mail RSS


Analysis of Fixing Nodes Used in Generalized Inverse Computation

Pavla Hruskova

DOI: 10.15598/aeee.v12i2.1020


Abstract

In various fields of numerical mathematics, there arises the need to compute a generalized inverse of a symmetric positive semidefinite matrix, for example in the solution of contact problems. Systems with semidefinite matrices can be solved by standard direct methods for the solution of systems with positive definite matrices adapted to the solution of systems with only positive semidefinite matrix. One of the possibilities is a modification of Cholesky decomposition using so called fixing nodes, which is presented in this paper with particular emphasise on proper definition of fixing nodes. The generalised inverse algorithm consisting in Cholesky decomposition with usage of fixing nodes is adopted from paper [1]. In [1], authors choose the fixing nodes using Perron vector of an adjacency matrix of the graph which is only a sub-optimal choice. Their choice is discussed in this paper together with other possible candidates on fixing node. Several numerical experiments including all candidates have been done. Based on these results, it turns out that using eigenvectors of Laplacian matrix provides better choice of fixing node than using Perron vector.

Keywords


Cholesky decomposition; fixing nodes; generalised inverse; Laplacian matrix; spectral graph theory; stiffness matrix.

Full Text:

PDF