Nonlinear fractal interpolation curves with function vertical scaling factors

Kim, JinMyong; Kim, HyonJin; Mun, Hakmyong

doi:10.1007/s13226-020-0412-x

Cited by 15 publications

(6 citation statements)

References 11 publications

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“…If a compatibility condition is satisfied, then there exists exactly one bounded ϕ : X → Y which satisfies the system (6). The function ϕ is given by…”

Section: Corollary 1 In the Conditions Of Theorem 2 The Number Of Solutions ϕ Of Problem (1) Is Equal To The Number Of Distinct Functionsmentioning

confidence: 99%

“…The corresponding fractal interpolation functions arise as solutions of a specific type of iterative functional equations, namely affine systems. Further developments and generalizations quickly arose in the scientific literature [6][7][8]. A class of these systems of iterative functional equations (the special case of fractal interpolation without explicit dependence on the independent variable) corresponds to the solution of conjugacy equations (see e.g.…”

Section: Introductionmentioning

confidence: 99%

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Compatibility Conditions for Systems of Iterative Functional Equations with Non-trivial Contact Sets

Buescu

Serpa

2021

Results Math

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Systems of iterative functional equations with a non-trivial set of contact points are not necessarily solvable, as the resulting intersections may lead to an overdetermination of the system. To obtain existence and uniqueness results additional conditions must be imposed on the system. These are the compatibility conditions, which we define and study in a general setting. An application to the affine and doubly affine cases allows us to solve an open problem in the theory of functional equations. In the last section we consider a special problem in a different perspective, showing that a complex compatibility condition may result in an elegant and simple property of the solution.

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“…If a compatibility condition is satisfied, then there exists exactly one bounded ϕ : X → Y which satisfies the system (6). The function ϕ is given by…”

Section: Corollary 1 In the Conditions Of Theorem 2 The Number Of Solutions ϕ Of Problem (1) Is Equal To The Number Of Distinct Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Compatibility Conditions for Systems of Iterative Functional Equations with Non-trivial Contact Sets

Buescu

Serpa

2021

Results Math

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“…A recent direction of research to obtain more general FIF is to replace the classical Banach contraction principle with more relaxed fixed point results, thus obtaining a wider spectrum of FIFs. In this respect, the reader is encouraged to refer to [30][31][32], for instance. The concept of FIF has been extended by Secelean (see [33]) to countable systems of data by using countable iterated function systems, or CIFS, for short.…”

Section: Introductionmentioning

confidence: 99%

Scale-Free Fractal Interpolation

2022

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An iterated function system that defines a fractal interpolation function, where ordinate scaling is replaced by a nonlinear contraction, is investigated here. In such a manner, fractal interpolation functions associated with Matkowski contractions for finite as well as infinite (countable) sets of data are obtained. Furthermore, we construct an extension of the concept of α-fractal interpolation functions, herein called R-fractal interpolation functions, related to a finite as well as to a countable iterated function system and provide approximation properties of the R-fractal functions. Moreover, we obtain smooth R-fractal interpolation functions and provide results that ensure the existence of differentiable R-fractal interpolation functions both for the finite and the infinite (countable) cases.

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“…However, the existing interpolation algorithms ignore the effect of the nonlinear variation of the radio frequency signal on the interpolation accuracy, resulting in low interpolation accuracy. To this end, many scholars have proposed a variety of sensor nonlinear compensation methods [13,14]. en, the signal feature quantity does not conform to the linear distribution due to a complex environment or a large distance between acquisition points; the nonlinear interpolation algorithm can be used to accurately calculate the signal feature statistics between the points according to the nonlinear distribution law, allowing the location of the anchor point to be determined.…”

Section: Introductionmentioning

confidence: 99%

Fixed Assets Positioning Management Based on Nonlinear Difference Algorithm

2022

Mobile Information Systems

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Fixed assets are an enterprise’s core means of production and a vital asset for the enterprise’s sustainability. Good fixed asset management not only helps to enhance asset utilization but also helps to prevent idleness and asset loss, both of which are vital in the success of the enterprise. To improve fixed asset management, it needs not only a good asset management system but also advanced asset monitoring and management technology. As a result, to address the issues of difficult positioning, tracking, and low management efficiency in enterprise’s asset management, this paper optimizes the commonly used the LANDMARC positioning algorithm and implements an improved algorithm based on Lagrange nonlinear interpolation. It is also used in fixed asset positioning management to overcome the problem of increasing the density of auxiliary tags to enhance positioning accuracy, which leads to higher costs and greater radio frequency interference. Simultaneously, a set of RFID-based fixed asset management systems was built and implemented, starting with the application requirements of enterprises and combining the optimization algorithm with FRID technology. Finally, a simulation experiment on the application of the Lagrange nonlinear interpolation algorithm in fixed asset positioning management is carried out and a comparison with other algorithms is performed. According to the simulation findings, the new algorithm has enhanced the positioning accuracy. The system can perform all-around dynamic tracking and positioning management of diverse assets, optimize the use efficiency and management level of assets, and improve the intelligent level of enterprise asset management.

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Nonlinear fractal interpolation curves with function vertical scaling factors

Cited by 15 publications

References 11 publications

Compatibility Conditions for Systems of Iterative Functional Equations with Non-trivial Contact Sets

Compatibility Conditions for Systems of Iterative Functional Equations with Non-trivial Contact Sets

Scale-Free Fractal Interpolation

Fixed Assets Positioning Management Based on Nonlinear Difference Algorithm

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