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Explicit solutions of infinite linear systems associated with group inverse endomorphisms

Fernando Pablos Romo (2022)

Czechoslovak Mathematical Journal

The aim of this note is to offer an algorithm for studying solutions of infinite linear systems associated with group inverse endomorphisms. As particular results, we provide different properties of the group inverse and we characterize EP endomorphisms of arbitrary vector spaces from the coincidence of the group inverse and the Moore-Penrose inverse.

Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems

Raheleh Shokrpour, Ghodrat Ebadi (2022)

Applications of Mathematics

Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew-Hermitian positive definite and positive semi-definite splitting (EHPPS) iterative method and extrapolated triangular positive definite and positive semi-definite splitting (ETPPS) iterative method. We also investigate convergence analysis and consistency of the...

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.

Maximal solutions of two–sided linear systems in max–min algebra

Pavel Krbálek, Alena Pozdílková (2010)

Kybernetika

Max-min algebra and its various aspects have been intensively studied by many authors [1, 4] because of its applicability to various areas, such as fuzzy system, knowledge management and others. Binary operations of addition and multiplication of real numbers used in classical linear algebra are replaced in max-min algebra by operations of maximum and minimum. We consider two-sided systems of max-min linear equations A ⊗ x = B ⊗ x , with given coefficient matrices A and B . We present a polynomial method for...

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.

Minimizing and maximizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint

Zofia Matusiewicz (2022)

Kybernetika

This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to max - * fuzzy relational equations and an inequality constraint, where * is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint,...

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