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Title: Interval solutions of linear interval equations (English)
Author: Rohn, Jiří
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 35
Issue: 3
Year: 1990
Pages: 220-224
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: linear systems
Keyword: interval arithmetic
Keyword: interval solution
Keyword: interval matrix
Keyword: interval vector
MSC: 15A06
MSC: 65F30
MSC: 65G10
MSC: 65G30
MSC: 65H05
MSC: 65H10
idZBL: Zbl 0716.65047
idMR: MR1052743
DOI: 10.21136/AM.1990.104406
Date available: 2008-05-20T18:39:19Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] W. Barth E. Nuding: Optimale Lösung von Intervallgleichungssystemen.Computing 12 (1974), 117-125. MR 0398075, 10.1007/BF02260368
Reference: [2] H. Beeck: Zur Problematik der Hüllenbestimmung von Interval Mathematics (K. Nickel, Ed.). Lecture Notes, Springer 1975, 150-159. Zbl 0303.65025, 10.1007/3-540-07170-9_12
Reference: [3] E. Hansen: On Linear Algebraic Equations with Interval Topics in Interval Analysis (E. Hansen, Ed.). Clarendon Press, Oxford 1969.
Reference: [4] R. E. Moore: Interval Analysis.Prentice-Hall, Englewood Cliffs 1966. Zbl 0176.13301, MR 0231516
Reference: [5] K. Nickel: Die Auflösbarkeit linearer Kreisscheiben- und Intervall-Gleichungssysteme.Freiburger Intervall-Berichte 81/3, 11 - 46. Zbl 0483.65019
Reference: [6] W. Oettli W. Prager: Compatibility of Approximate Solution of Linear Equations with Given Error Bounds for Coefficients and Right-Hand Sides.Numerische Mathematik 6 (1964), 405-409. MR 0168106, 10.1007/BF01386090
Reference: [7] H. Ratschek W. Sauer: Linear Interval Equations.Computing 28 (1982), 105-115. MR 0653366, 10.1007/BF02241817
Reference: [8] J. Rohn: Some Results on Interval Linear Systems.Freiburger Intervall-Berichte 85/4, 93-116.
Reference: [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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