Regular matrix of interval numbers based on Fibonacci numbers (original) (raw)

2014, Afrika Matematika

https://doi.org/10.1007/S13370-014-0289-0

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Abstract

The main purpose of this paper is to introduce the criterion for the regularity of a matrix whose elements are interval numbers and define a regular matrixF of interval numbers using fibonacci numbers and to introduce some new sequence spaces c i 0 (F), c i (F), l i ∞ (F) based on the newly defined regular matrix of interval numbersF and investigate some relations related to these spaces.

On Relation Between P-Matrices and Regularity of Interval Matrices

Springer Proceedings in Mathematics & Statistics, 2017

We explore new results between P-matrix property and regularity of interval matrices. In particular, we show that an interval matrix is regular in and only if some special matrices constructed from its center and radius matrices are P-matrices. We also investigate the converse direction. We reduce the problem of checking P-matrix property to regularity of a special interval matrix. Based on this reduction, novel sufficient condition for a P-matrix property is derived, and its strength is inspected. We also state a new observation to interval P-matrices.

On The Spaces of Fibonacci Difference Null and Convergent Sequences

2013

In the present paper, by using the band matrix F defined by the Fibonacci sequence, we introduce the sequence sequence spaces c_0(F) and c(F). Also, we give some inclusion relations and construct the bases of the spaces c_0(F) and c(F). Finally, we compute the alpha-, beta-, gamma-duals of these spaces and characterize the classes (c_0(F),X) and (c(F),X) for certain choice of the sequence space X.

A New Sufficient Condition for Regularity of Interval Matrices

We present a sufficient regularity condition for interval matrices which generalizes two previously known ones. It is formulated in terms of positive definiteness of a certain point matrix, and can also be used for checking positive definiteness of interval matrices. Comparing it with Beeck's strong regularity condition, we show by counterexamples that none of the two conditions is more general than the other one. Above: logo of interval computations and related areas (depiction of the solution set of the system [2, 4]x 1 + [−2, 1]x 2 = [−2, 2], [−1, 2]x 1 + [2, 4]x 2 = [−2, 2] (Barth and Nuding [1])).

Generalized Fibonacci and k-Pell Matrix Sequences

2018

In the present article first and foremost we define generalized Fibonacci sequence and k-Pell sequence. After that by using these sequences we delineate generalized Fibonacci matrix sequence and k-Pell matrix sequence. At the hindmost we obtain results by some matrix technique for both general sequences as well as for matrix sequences. AMS (MOS) Subject Classification Codes: 11B37; 11B39; 15A15.

Matrices with the consecutive ones property, interval graphs and their applications

2001

Matrices with the consecutive ones property and interval graphs are important notations in the field of applied mathematics. We give a theoretical picture of them in first part. We present the earliest work in interval graphs and matrices with the consecutive ones property pointing out the close relation between them. We pay attention to Tucker's structure theorem on matrices with the consecutive ones property as an essential step that requires a deep considerations. Later on we concentrate on some recent work characterizing the matrices with the consecutive ones property and matrices related to them in the terms of interval digraphs as the latest and most interesting outlook on our topic. Within this framework we introduce a classiffcation of matrices with consecutive ones property and matrices related to them. We describe the applications of matrices with the consecutive ones property and interval graphs in different fields. We make sure to give a general view of application a...

On some double sequence spaces of interval number

Proyecciones (Antofagasta)

Esi and Yasemin [9] defined the metric spaces c 0 (f, p, s), c(f, p, s), l ∞ (f, p, s) and l p (f, p, s) of sequences of interval numbers by a modulus function. In this study, we consider a generalization for double sequences of these metric spaces by taking a ψ function, satisfying the following conditions, instead of s parameter. For this aim, let ψ(k, l) be a positive function for all k, l ∈ N such that (i) lim k,l→∞ ψ(k, l) = 0, (ii) ∆ 2 ψ(k, l) = ψ(k − 1, l − 1) − 2ψ(k, l) + ψ(k + 1, l + 1) ≥ 0. or ψ(k, l) = 1. Therefore, according to class of functions which satisfying the conditions (i) and (ii) we deal with the metric spaces c 2 0 (f, p, ψ), c 2 (f, p, ψ), l 2 ∞ (f, p, ψ) and l 2 p (f, p, ψ) of double sequences of interval numbers defined by a modulus function.

Some Results on Interval-ValuedFuzzy Matrices

Proceedings of the 2010 International Conference on E-Business Intelligence, 2010

In this paper, we introduced intervalvalued fuzzy matrices (IVFMs) as the generalization of interval-valued fuzzy sets. Some essential unary and binary operations of IVFM and some special types of IVFMs i.e., symmetric, reflexive, transitive and idempotent, constant, etc. are defined here. The idea of convergence, periodicity, determinant and adjoint of IVFMs are also defined. Lot of properties of IVFMs are presented here.

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Some Newly Defined Sequence Spaces Using Regular Matrix of Fibonacci Numbers

Afyon Kocatepe University Journal of Sciences and Engineering, 2014

The main purpose of this paper is to introduce the new sequence spaces (F), c(F) and (F) based on the newly defined regular matrix F of Fibonacci numbers. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces.

On some difference sequence spaces of interval numbers

Proyecciones (Antofagasta)

In this paper we introduce the sequence spaces c 0 i (∆) ,c i (∆) and i ∞ (∆) of interval numbers and study some of their algebraic and topological properties. Also we investigate some inclusion relations related to these spaces.

On Some Properties of Interval Matrices

2007

By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations. Keywords—Interval arithmetic, Interval matrix, linear equations.

A note on checking regularity of interval matrices

Linear and Multilinear Algebra, 1995

It is proved that two previously known sufficient conditions for regularity of interval matrices are equivalent in the sense that they cover the same class of interval matrices.

An Overview of Polynomially Computable Characteristics of Special Interval Matrices

Studies in Computational Intelligence, 2020

It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying polynomially solvable classes thus belongs to important current trends. The purpose of this paper is to review some of such classes. In particular, we focus on several special interval matrices and investigate their convenient properties. We consider tridiagonal matrices, {M,H,P,B}-matrices, inverse M-matrices, inverse nonnegative matrices, nonnegative matrices, totally positive matrices and some others. We focus in particular on computing the range of the determinant, eigenvalues, singular values, and selected norms. Whenever possible, we state also formulae for determining the inverse matrix and the hull of the solution set of an interval system of linear equations. We survey not only the known facts, but we present some new views as well.

ON THE SPACES OF FIBONACCI DIFFERENCE ABSOLUTELY p-SUMMABLE, NULL AND CONVERGENT SEQUENCES

Sarajevo Journal of Mathematics, 2016

Let 0 < p < 1. In the present paper, as the domain of the band matrix F defined by the Fibonacci sequence in the classical sequence spaces p, c0 and c, we introduce the sequence spaces p( F ), c0( F ) and c( F ), respectively. Also, we give some inclusion relations and construct the bases of the spaces c0( F ) and c( F ). Finally, we compute the alpha, beta, gamma duals of these spaces and characterize the classes ( p( F ), µ) of infinite matrices with µ ∈ { ∞, c, c0}.

AE Regularity of Interval Matrices

The Electronic Journal of Linear Algebra, 2018

Consider a linear system of equations with interval coefficients, and each interval coefficient is associated with either a universal or an existential quantifier. The AE solution set and AE solvability of the system is defined by ∀∃- quantification. The paper deals with the problem of what properties must the coefficient matrix have in order that there is guaranteed an existence of an AE solution. Based on this motivation, a concept of AE regularity is introduced, which implies that the AE solution set is nonempty and the system is AE solvable for every right-hand side. A characterization of AE regularity is discussed, and also various classes of matrices that are implicitly AE regular are investigated. Some of these classes are polynomially decidable, and therefore give an efficient way for checking AE regularity. Eventually, there are also stated open problems related to computational complexity and characterization of AE regularity.

A new Fibonacci matrix definition and some results

Matrix Science Mathematic, 2024

A new definition of the Fibonacci Matrix is given. The elements of the matrix consist of the Fibonacci numbers. First a preliminary knowledge on Fibonacci sequences and their properties are given. Then the new definition of the matrix is given together with some properties. The difference from the common definition is also discussed. The determinant of the matrix and its properties are posed and proven. Applications to systems of algebraic equations are also outlined.

Compact operators on some Fibonacci difference sequence spaces

Journal of Inequalities and Applications, 2015

In this paper, we characterize the matrix classes (1 , p (F)) (1 ≤ p < ∞), where p (F) is some Fibonacci difference sequence spaces. We also obtain estimates for the norms of the bounded linear operators L A defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.