Interval solutions of linear interval equations

Jiří Rohn

Aplikace matematiky (1990)

  • Volume: 35, Issue: 3, page 220-224
  • ISSN: 0862-7940

Abstract

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It is shown that if the concept of an interval solution to a system of linear interval equations given by Ratschek and Sauer is slightly modified, then only two nonlinear equations are to be solved to find a modified interval solution or to verify that no such solution exists.

How to cite

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Rohn, Jiří. "Interval solutions of linear interval equations." Aplikace matematiky 35.3 (1990): 220-224. <http://eudml.org/doc/15627>.

@article{Rohn1990,
abstract = {It is shown that if the concept of an interval solution to a system of linear interval equations given by Ratschek and Sauer is slightly modified, then only two nonlinear equations are to be solved to find a modified interval solution or to verify that no such solution exists.},
author = {Rohn, Jiří},
journal = {Aplikace matematiky},
keywords = {linear systems; interval arithmetic; interval solution; interval matrix; interval vector; linear interval equations; interval solution; interval matrix; interval vector},
language = {eng},
number = {3},
pages = {220-224},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Interval solutions of linear interval equations},
url = {http://eudml.org/doc/15627},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Rohn, Jiří
TI - Interval solutions of linear interval equations
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 3
SP - 220
EP - 224
AB - It is shown that if the concept of an interval solution to a system of linear interval equations given by Ratschek and Sauer is slightly modified, then only two nonlinear equations are to be solved to find a modified interval solution or to verify that no such solution exists.
LA - eng
KW - linear systems; interval arithmetic; interval solution; interval matrix; interval vector; linear interval equations; interval solution; interval matrix; interval vector
UR - http://eudml.org/doc/15627
ER -

References

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  1. W. Barth E. Nuding, 10.1007/BF02260368, Computing 12 (1974), 117-125. (1974) Zbl0275.65008MR0398075DOI10.1007/BF02260368
  2. H. Beeck, Zur Problematik der Hüllenbestimmung von Intervallgleichungssystemen, in: Interval Mathematics (K. Nickel, Ed.). Lecture Notes, Springer 1975, 150-159. (1975) Zbl0303.65025
  3. E. Hansen, On Linear Algebraic Equations with Interval Coefficients, in: Topics in Interval Analysis (E. Hansen, Ed.). Clarendon Press, Oxford 1969. (1969) Zbl0185.40201
  4. R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs 1966. (1966) Zbl0176.13301MR0231516
  5. K. Nickel, Die Auflösbarkeit linearer Kreisscheiben- und Intervall-Gleichungssysteme, Freiburger Intervall-Berichte 81/3, 11 - 46. Zbl0483.65019
  6. W. Oettli W. Prager, 10.1007/BF01386090, Numerische Mathematik 6 (1964), 405-409. (1964) Zbl0133.08603MR0168106DOI10.1007/BF01386090
  7. H. Ratschek W. Sauer, 10.1007/BF02241817, Computing 28 (1982), 105-115. (1982) Zbl0468.65025MR0653366DOI10.1007/BF02241817
  8. J. Rohn, Some Results on Interval Linear Systems, Freiburger Intervall-Berichte 85/4, 93-116. 
  9. J. Rohn, A Note on Solving Equations of Турe A 1 x 1 = b 1 , Freiburger Intervall-Berichte 86/4, 29-31. 

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