Generalization of the minimax method for calculation of the spectral radius of a matrix

Jan Zítko

Aplikace matematiky (1970)

  • Volume: 15, Issue: 1, page 41-62
  • ISSN: 0862-7940

Abstract

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Let B be a non-negative irreducible n × n cyclic matrix of index 2, let I be the unite matrix. In this paper the calculation of the spectral radius of the matrix B + α I by minimax method as well as the rate of convergence in dependence on the number α is studied.

How to cite

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Zítko, Jan. "Generalization of the minimax method for calculation of the spectral radius of a matrix." Aplikace matematiky 15.1 (1970): 41-62. <http://eudml.org/doc/14629>.

@article{Zítko1970,
abstract = {Let $B$ be a non-negative irreducible $n\times n$ cyclic matrix of index 2, let $I$ be the unite matrix. In this paper the calculation of the spectral radius of the matrix $B+\alpha I$ by minimax method as well as the rate of convergence in dependence on the number $\alpha $ is studied.},
author = {Zítko, Jan},
journal = {Aplikace matematiky},
keywords = {numerical mathematics},
language = {eng},
number = {1},
pages = {41-62},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalization of the minimax method for calculation of the spectral radius of a matrix},
url = {http://eudml.org/doc/14629},
volume = {15},
year = {1970},
}

TY - JOUR
AU - Zítko, Jan
TI - Generalization of the minimax method for calculation of the spectral radius of a matrix
JO - Aplikace matematiky
PY - 1970
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 15
IS - 1
SP - 41
EP - 62
AB - Let $B$ be a non-negative irreducible $n\times n$ cyclic matrix of index 2, let $I$ be the unite matrix. In this paper the calculation of the spectral radius of the matrix $B+\alpha I$ by minimax method as well as the rate of convergence in dependence on the number $\alpha $ is studied.
LA - eng
KW - numerical mathematics
UR - http://eudml.org/doc/14629
ER -

References

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  1. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey 1962. (1962) MR0158502
  2. D. M. Young, 10.1090/S0002-9947-1954-0059635-7, Trans. Amer. Math. Soc. 76 (1954), 92-111. (1954) Zbl0055.35704MR0059635DOI10.1090/S0002-9947-1954-0059635-7
  3. E. Humhal, J. Zítko, Poznámka k superrelaxační metodě, Aplikace matematiky 3, sv. 12 (1967) 161-170. (1967) MR0224263
  4. J. Zítko, Srovnání metod pro výpočet spektrálního poloměru matice, Sborník výzkumných prací Ústavu výpočtové techniky ČSAV - ČVUT 1967. (1967) 

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