A Countable Fractal Interpolation Scheme Involving Rakotch Contractions
Sign Up to like & getrecommendations! Published in 2021 at "Results in Mathematics"
DOI: 10.1007/s00025-021-01470-x
Abstract: The main result of this paper states that for a given countable system of data ∆, there exists a countable iterated function system consisting of Rakotch contractions, such that its attractor is the graph of… read more here.
Keywords: consisting rakotch; countable fractal; fractal interpolation; rakotch contractions ... See more keywords
Constrained and convex interpolation through rational cubic fractal interpolation surface
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DOI: 10.1007/s40314-018-0689-0
Abstract: A new $${\mathcal {C}}^1$$C1-rational cubic fractal interpolation surface is introduced to interpolate the surface data which lies on a rectangular grid. At the beginning, $${\mathcal {C}}^1$$C1-rational cubic fractal interpolation functions are constructed along the grid… read more here.
Keywords: surface; interpolation surface; rational cubic; interpolation ... See more keywords
Dimension analysis for Caputo-fractional derivative of spline fractal interpolation function
Sign Up to like & getrecommendations! Published in 2024 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2024.2435014
Abstract: The fractal dimension is an indispensable tool bridging the two distinct fields of mathematics namely, the fractional calculus and the fractal geometry. Many works have elucidated a linear connection between the order of fractional calculus… read more here.
Keywords: caputo fractional; interpolation function; fractional derivative; dimension ... See more keywords
Parameter Identification for a Class of Bivariate Fractal Interpolation Functions and Constrained Approximation
Sign Up to like & getrecommendations! Published in 2020 at "Numerical Functional Analysis and Optimization"
DOI: 10.1080/01630563.2020.1738458
Abstract: Abstract The current article intends to study some elementary constrained approximation aspects of the bivariate fractal functions. To this end, firstly the construction of bivariate fractal interpolation functions available in the literature is revisited with… read more here.
Keywords: interpolation functions; constrained approximation; bivariate fractal; bivariate ... See more keywords
STATISTICAL PROPERTIES OF LINEAR FRACTAL INTERPOLATION FUNCTIONS FOR RANDOM DATA SETS
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DOI: 10.1142/s0218348x18500093
Abstract: Let N be an integer greater than or equal to 2 and let xi′s be numbers with x0 < x1 < x2 < ⋯ < xN. Denote that I is the interval [x0,xN] and Δ… read more here.
Keywords: interpolation functions; linear fractal; properties linear; statistical properties ... See more keywords
RECURRENT FRACTAL INTERPOLATION SURFACES ON TRIANGULAR DOMAINS
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DOI: 10.1142/s0218348x19500853
Abstract: We present a general framework to construct recurrent fractal interpolation surfaces (RFISs) on triangular domains. Then we introduce affine RFISs, which are easy to be generated while there are no restrictions on interpolation points and… read more here.
Keywords: triangular domains; interpolation surfaces; recurrent fractal; surfaces triangular ... See more keywords
SUPER COALESCENCE HIDDEN-VARIABLE FRACTAL INTERPOLATION FUNCTIONS
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DOI: 10.1142/s0218348x21500511
Abstract: In this paper, a new notion of super coalescence hidden-variable fractal interpolation function (SCHFIF) is introduced. The construction of SCHFIF involves choosing an IFS from a pool of several non-diagonal IFS at each level of… read more here.
Keywords: super coalescence; hidden variable; interpolation; coalescence hidden ... See more keywords
The Application of a Complex Composite Fractal Interpolation Algorithm in the Seabed Terrain Simulation
Sign Up to like & getrecommendations! Published in 2018 at "Mathematical Problems in Engineering"
DOI: 10.1155/2018/8641471
Abstract: Seabed terrain modelling is one of the key technologies in the Subsea Environmental Information System, and this system is critical for underwater vehicle path planning. A composite fractal interpolation algorithm based on improved fractional Brownian… read more here.
Keywords: interpolation algorithm; seabed terrain; interpolation; composite fractal ... See more keywords
Improve fractal interpolation function with Sierspinski triangle
Sign Up to like & getrecommendations! Published in 2024 at "Indonesian Journal of Electrical Engineering and Computer Science"
DOI: 10.11591/ijeecs.v36.i3.pp1485-1492
Abstract: Interpolation techniques can be used to determine the approximate value of a parameter if it is known that two values are bound to a certain interval. Interpolation can be done numerically or fractal. The fractal… read more here.
Keywords: interpolation function; value; mape; fractal interpolation ... See more keywords
On bivariate fractal interpolation for countable data and associated nonlinear fractal operator
Sign Up to like & getrecommendations! Published in 2024 at "Demonstratio Mathematica"
DOI: 10.1515/dema-2024-0014
Abstract: Abstract Fractal interpolation has been conventionally treated as a method to construct a univariate continuous function interpolating a given finite data set with the distinguishing property that the graph of the interpolating function is the… read more here.
Keywords: function; fractal interpolation; associated nonlinear; bivariate fractal ... See more keywords
A controlled fractal interpolation method based on random midpoint displacement for coastline
Sign Up to like & getrecommendations! Published in 2017 at "Geoinformatica"
DOI: 10.5623/cig2017-202
Abstract: Coastline has different geographical bending characteristics in different coastal geomorphic regions. The existing fractal interpolation methods for coastline mostly focus on how to simulate its fractal characteristic but neglect the geographical bending characteristic. This study… read more here.
Keywords: method based; controlled fractal; coastline; bending characteristics ... See more keywords