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Computing and Visualizing Solution Sets of Interval Linear Systems

Krämer, Walter (2007)

Serdica Journal of Computing

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006The computation of the exact solution set of an interval linear system is a nontrivial task [2, 13]. Even in two and three dimensions a lot of work has to be done. We demonstrate two different realizations. The first approach (see [16]) is based on Java, Java3D, and the BigRational package [21]. An applet allows modifications of the matrix coefficients and/or the coefficients...

Ein effizienter Algorithmus zur iterativen Einschliessung der inversen Matrix

Jürgen Herzberger (1987)

Aplikace matematiky

Es wird ein kombinierter Algorithmus zur iterativen Einschlissung der Inversen einer Matrix beschrieben. Es handelt sich dabei um eine intervallmässige Version des Schulz'schen Verfahrens. Es wird bewiesen, dass der Algorithmus genauso effizient ist wie ein hisher bekannter aus [2], dass er aber in Bezug auf den akkumulierten Rundungsfehler dem bisherigen Vorgehen vorzuziehen ist. Ein numerisches Beispiel wird gegeben.

Enclosures for the solution set of parametric interval linear systems

Milan Hladík (2012)

International Journal of Applied Mathematics and Computer Science

We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods....

Interval algorithm for absolute value equations

Aixiang Wang, Haijun Wang, Yongkun Deng (2011)

Open Mathematics

We investigate the absolute value equations Ax−|x| = b. Based on ɛ-inflation, an interval verification method is proposed. Theoretic analysis and numerical results show that the new proposed method is effective.

Interval fuzzy matrix equations

Emília Draženská, Helena Myšková (2017)

Kybernetika

This paper deals with the solvability of interval matrix equations in fuzzy algebra. Fuzzy algebra is the algebraic structure in which the classical addition and multiplication are replaced by maximum and minimum, respectively. The notation 𝐀 ⊗ X ⊗ 𝐂 = 𝐁 , where 𝐀 , 𝐁 , 𝐂 are given interval matrices and X is an unknown matrix, represents an interval system of matrix equations. We can define several types of solvability of interval fuzzy matrix equations. In this paper, we shall deal with four of them. We define the...

Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem

Sedighe Khaleghzade, Mostafa Zangiabadi, Aljoša Peperko, Masoud Hajarian (2022)

Kybernetika

In this paper, we propose the notions of the max-plus algebra of the interval tensors, which can be used for the extension of interval linear systems to interval multi-linear systems in the max-plus algebra. Some properties and basic results of interval multi-linear systems in max-plus algebra are derived. An algorithm is developed for computing a solution of the multi-linear systems in the max-plus algebra. Necessary and sufficient conditions for the interval multi-linear systems for weak solvability...

Interval solutions of linear interval equations

Jiří Rohn (1990)

Aplikace matematiky

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.

Max-min interval systems of linear equations with bounded solution

Helena Myšková (2012)

Kybernetika

Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗ , where a ⊕ b = max { a , b } , a ⊗ b = min { a , b } . The notation 𝐀 ⊗ 𝐱 = 𝐛 represents an interval system of linear equations, where 𝐀 = [ A ̲ , A ¯ ] , 𝐛 = [ b ̲ , b ¯ ] are given interval matrix and interval vector, respectively, and a solution is from a given interval vector 𝐱 = [ x ̲ , x ¯ ] . We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them.

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