Hidden Variable Fractal Interpolation Functions

1989 ◽  
Vol 20 (5) ◽  
pp. 1218-1242 ◽  
Author(s):  
M. F. Barnsley ◽  
J. Elton ◽  
D. Hardin ◽  
P. Massopust
Keyword(s):  
Fractal Interpolation ◽  
Hidden Variable ◽  
Fractal Interpolation Functions ◽  
Interpolation Functions

CONSTRUCTION OF NONLINEAR HIDDEN VARIABLE FRACTAL INTERPOLATION FUNCTIONS AND THEIR STABILITY

Fractals ◽  
2019 ◽  
Vol 27 (06) ◽  
pp. 1950103
Author(s):  
JINMYONG KIM ◽  
HYONJIN KIM ◽  
HAKMYONG MUN
Keyword(s):  
Iterated Function Systems ◽  
Continuous Functions ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Hidden Variable ◽  
Fractal Interpolation Functions ◽  
The Stability ◽  
And Function ◽  
Stability Results ◽  
Interpolation Functions

This paper presents a method to construct nonlinear hidden variable fractal interpolation functions (FIFs) and their stability results. We ensure that the projections of attractors of vector-valued nonlinear iterated function systems (IFSs) constructed by Rakotch contractions and function vertical scaling factors are graphs of some continuous functions interpolating the given data. We also give an explicit example illustrating obtained results. Then, we get the stability results of the constructed FIFs in the case of the generalized interpolation data having small perturbations.

scholarly journals Multiresolution Analysis Based on Coalescence Hidden-Variable Fractal Interpolation Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
G. P. Kapoor ◽  
Srijanani Anurag Prasad
Keyword(s):  
Vector Space ◽  
Multiresolution Analysis ◽  
Riesz Bases ◽  
Fractal Interpolation ◽  
Hidden Variable ◽  
Free Variables ◽  
Fractal Interpolation Functions ◽  
Interpolation Functions ◽  
Vector Subspaces

Multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is developed. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(R) than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). Our approach consists of introduction of the vector space of CHFIFs, determination of its dimension and construction of Riesz bases of vector subspaces Vk, k∈Z, consisting of certain CHFIFs in L2(R)∩C0(R).

SENSITIVITY ANALYSIS FOR HIDDEN VARIABLE FRACTAL INTERPOLATION FUNCTIONS AND THEIR MOMENTS

Fractals ◽  
2009 ◽  
Vol 17 (02) ◽  
pp. 161-170
Author(s):  
HONG-YONG WANG
Keyword(s):  
Sensitivity Analysis ◽  
Iterated Function System ◽  
Fractal Interpolation ◽  
Hidden Variable ◽  
Fractal Interpolation Functions ◽  
Iterated Function ◽  
The Difference ◽  
The Moment ◽  
Upper Estimate ◽  
Interpolation Functions

The sensitivity analysis for a class of hidden variable fractal interpolation functions (HVFIFs) and their moments is made in the work. Based on a vector valued iterated function system (IFS) determined, we introduce a perturbed IFS and investigate the relations between the two HVFIFs generated by the IFS determined and its perturbed IFS, respectively. An explicit expression for the difference between the two HVFIFs is presented, from which, we show that the HVFIFs are not sensitive to a small perturbation in IFSs. Furthermore, we compute the moment integrals of the HVFIFs and discuss the error of moments of the two HVFIFs. An upper estimate for the error is obtained.

scholarly journals Reproducing Kernel Hilbert Space and Coalescence Hidden-variable Fractal Interpolation Functions

2019 ◽  
Vol 52 (1) ◽  
pp. 467-474
Author(s):  
Srijanani Anurag Prasad
Keyword(s):  
Hilbert Spaces ◽  
Complex Analysis ◽  
Reproducing Kernel ◽  
Group Representation ◽  
Reproducing Kernel Hilbert Space ◽  
Fractal Interpolation ◽  
Hidden Variable ◽  
Fractal Interpolation Functions ◽  
Kernel Hilbert Spaces ◽  
Interpolation Functions

AbstractReproducing Kernel Hilbert Spaces (RKHS) and their kernel are important tools which have been found to be incredibly useful in many areas like machine learning, complex analysis, probability theory, group representation theory and the theory of integral operator. In the present paper, the space of Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is demonstrated to be an RKHS and its associated kernel is derived. This extends the possibility of using this new kernel function, which is partly self-affine and partly non-self-affine, in diverse fields wherein the structure is not always self-affine.

HIDDEN VARIABLE VECTOR VALUED FRACTAL INTERPOLATION FUNCTIONS

Fractals ◽  
2005 ◽  
Vol 13 (03) ◽  
pp. 227-232 ◽  
Author(s):  
P. BOUBOULIS ◽  
L. DALLA
Keyword(s):  
Fractal Interpolation ◽  
Random Grids ◽  
Hidden Variable ◽  
Fractal Interpolation Functions ◽  
Vector Valued ◽  
Interpolation Functions

We present a method of construction of vector valued bivariate fractal interpolation functions on random grids in ℝ2. Examples and applications are also included.

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