Barabanov norms, Lipschitz continuity and monotonicity for the max algebraic joint spectral radius

Guglielmi, Nicola; Mason, Oliver; Wirth, Fabian

doi:10.1016/j.laa.2018.01.042

Cited by 10 publications

(4 citation statements)

References 23 publications

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“…The algebraic system max algebra and its isomorphic versions (max plus algebra, tropical algebra) provide an attractive way of describing a class of nonlinear problems appearing for instance in manufacturing and transportation scheduling, information technology, discrete event dynamic systems, combinatorial optimization, mathematical physics, DNA analysis, ...(see e.g. [1,3,5,6,10,11] and the references cited there). It has been used to describe these conventionally nonlinear problems in a linear fashion.…”

Section: Introductionmentioning

confidence: 99%

On the numerical ranges of matrices in max algebra

Thaghizadeh

Zahraei

Peperko

et al. 2020

Banach J. Math. Anal.

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Let $$M_{n}({\mathbb {R}}_{+})$$ M n ( R + ) be the set of all $$n \times n$$ n × n nonnegative matrices. Recently, in Tavakolipour and Shakeri (Linear Multilinear Algebra 67, 2019, https://doi.org/10.1080/03081087.2018.1478946), the concept of the numerical range in tropical algebra was introduced and an explicit formula describing it was obtained. We study the isomorphic notion of the numerical range of nonnegative matrices in max algebra and give a short proof of the known formula. Moreover, we study several generalizations of the numerical range in max algebra. Let $$1 \le k \le n$$ 1 ≤ k ≤ n be a positive integer and $$C \in M_{ n}({\mathbb {R}}_{+}).$$ C ∈ M n ( R + ) . We introduce the notions of max $$k-$$ k - numerical range and max $$C-$$ C - numerical range. Some algebraic and geometric properties of them are investigated. Also, max numerical range $$W_\text {max}(\varSigma )$$ W max ( Σ ) of a bounded set $$\varSigma$$ Σ of $$n \times n$$ n × n nonnegative matrices is introduced and some of its properties are also investigated.

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Section: Introductionmentioning

confidence: 99%

On the numerical ranges of matrices in max algebra

Thaghizadeh

Zahraei

Peperko

et al. 2020

Banach J. Math. Anal.

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“…Together with its isomorphic versions (max-plus algebra and min-plus algebra also known as tropical algebra) it provides an attractive way of describing a class of non-linear problems appearing for instance in manufacturing and transportation scheduling, information technology, discrete event-dynamic systems, combinatorial optimization, mathematical physics, DNA analysis, ... (see e.g. [8], [11], [28], [27], [15], [34] and the references cited there).…”

Section: Resultsmentioning

confidence: 99%

Uniform Boundedness Principle for Nonlinear Operators on Cones of Functions

Peperko

2018

Journal of Function Spaces

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“…A conventional max algebra consists of the set of nonnegative real numbers equipped with the basic operations of multiplication a⊗b = ab, and maximization a ⊕ b = max{a, b} (see also e.g. [10], [7], [4], [1], [9] [14] and the references cited within). For A = (a ij ) ∈ M m×n (R), we say that A is positive (nonnegative) and write A > 0 (A ≥ 0) if a ij > 0 (a ij ≥ 0) for 1 ≤ i ≤ m, 1 ≤ j ≤ n. Let R + be the set of all nonnegative real numbers and M m×n (R + ) denote the set of all m × n nonnegative (real) matrices.…”

Section: Preliminariesmentioning

confidence: 99%

The Relationship of Family Affective Climate, Self-effectiveness, Personal-Social Adjustment with Academic Achievement of University Students: A Study in Islamic Azad University, Ahvaz, Iran

Safarzadeh¹

2016

PCP

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Objective: This research aimed to investigate the relationship of family affective climate, self-effectiveness, and personal-social adjustment variables with academic achievement of university students in Islamic Azad University, Ahvaz branch, Ahvaz, Iran. Methods:The research sample included 300 individuals (150 females and 150 males) who were selected through random stratified sampling method. California personal-social adjustment, Scherer and Adams self-effectiveness, and family's affective climate questionnaires were administered to collect the data. Correlation coefficient and linear regression analysis were used for analyzing the data. Results:The results of the data analysis indicated that there is a significant relationship between variables of family's affective climate, personal and social adjustment, and self-effectiveness with academic achievement of students (P<0.001). Furthermore, the results of linear regression analysis indicated that the variables of self-effectiveness, personal and social adjustment, and family's affective climate were significant predictors of academic achievement.Conclusion: Improving student's self-effectiveness, personal-social adjustment, and family's affective climate may have positive influences on their academic achievement.

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Barabanov norms, Lipschitz continuity and monotonicity for the max algebraic joint spectral radius

Cited by 10 publications

References 23 publications

On the numerical ranges of matrices in max algebra

On the numerical ranges of matrices in max algebra

Uniform Boundedness Principle for Nonlinear Operators on Cones of Functions

The Relationship of Family Affective Climate, Self-effectiveness, Personal-Social Adjustment with Academic Achievement of University Students: A Study in Islamic Azad University, Ahvaz, Iran

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