Options
Arya Kumar Bedabrata Chand
Loading...
Preferred name
Arya Kumar Bedabrata Chand
Official Name
Arya Kumar Bedabrata Chand
Alternative Name
Chand, Arya Kumar Bedabrata
Chand, Akb
Chand, Arya K.B.
Chand, A. K.B.
Main Affiliation
Email
ORCID
Scopus Author ID
Researcher ID
Google Scholar ID
15 results
Now showing 1 - 10 of 15
- PublicationA new class of fractal interpolation surfaces based on functional values(01-03-2016)
; Vijender, N.Fractal interpolation is a modern technique for fitting of smooth/non-smooth data. Based on only functional values, we develop two types of 1-rational fractal interpolation surfaces (FISs) on a rectangular grid in the present paper that contain scaling factors in both directions and two types of positive real parameters which are referred as shape parameters. The graphs of these 1-rational FISs are the attractors of suitable rational iterated function systems (IFSs) in R3 which use a collection of rational IFSs in the x-direction and y-direction and hence these FISs are self-referential in nature. Using upper bounds of the interpolation error of the x-direction and y-direction fractal interpolants along the grid lines, we study the convergence results of 1-rational FISs toward the original function. A numerical illustration is provided to explain the visual quality of our rational FISs. An extra feature of these fractal surface schemes is that it allows subsequent interactive alteration of the shape of the surfaces by changing the scaling factors and shape parameters. - PublicationPositive blending Hermite rational cubic spline fractal interpolation surfaces(01-03-2015)
; Vijender, N.Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. - PublicationBicubic partially blended rational fractal surface for a constrained interpolation problem(01-03-2018)
; ;Viswanathan, P.Vijender, N.This paper investigates some univariate and bivariate constrained interpolation problems using fractal interpolation functions. First, we obtain rational cubic fractal interpolation functions lying above a prescribed straight line. Using a transfinite interpolation via blending functions, we extend the properties of the univariate rational cubic fractal interpolation function to generate surfaces that lie above a plane. In particular, the constrained bivariate interpolation discussed herein includes a method to construct fractal interpolation surfaces that preserve positivity inherent in a prescribed data set. Uniform convergence of the bivariate fractal interpolant to the original function which generates the data is proven. - PublicationSHAPE PRESERVING ASPECTS of BIVARIATE α -FRACTAL FUNCTION(01-11-2021)
;Vijender, N.In this paper, we study shape preserving aspects of bivariate α-fractal functions. Its specific aims are: (i) to solve the range restricted problem for bivariate fractal approximation (ii) to establish the fractal analogue of lionized Weierstrass theorem of bivariate functions (iii) to study the constrained approximation by r-bivariate α-fractal functions (v) to investigate the conditions on the parameters of the iterated function system in order that the bivariate α-fractal function fα preserves fundamental shapes, namely, positivity and convexity (concavity) in addition to the smoothness of f over a rectangle (vi) to establish fractal versions of some elementary theorems in the shape preserving approximation of bivariate functions. - PublicationBivariate shape preserving interpolation: A fractal-classical hybrid approach(01-12-2015)
; ;Viswanathan, P.Vijender, N.The notion of cubic fractal interpolation function (FIF) has received considerable attention in the literature due to its versatility, flexibility and ease of implementation. In this article, we shall view cubic FIFs as a family of C1-continuous fractal functions associated with the traditional C1-continuous cubic spline. General theorems that identify suitable values of the parameters so as to constrain a fractal function and its first derivative within suitable axis-aligned rectangles are reported. By applying these theorems, cubic fractal interpolation of a data set subject to strip conditions on the interpolant and its first derivative is discussed. These results are applied to investigate positivity and monotonicity properties of a hybrid bivariate interpolant over a rectangular region R obtained by blending univariate cubic FIFs via bicubically blended Coons patch. The L∞-norm of the error in approximating a function f ∈ C2(R) with the proposed bivariate interpolant is shown to be of order O(h2) as h → 0. - PublicationA monotonic rational fractal interpolation surface and its analytical properties(01-01-2015)
; Vijender, N.A (Formula presented.)-continuous rational cubic fractal interpolation function was introduced and its monotonicity aspect was investigated in [Adv. Difference Eq. (30) 2014]. Using this univariate interpolant and a blending technique, in this article, we develop a monotonic rational fractal interpolation surface (FIS) for given monotonic surface data arranged on the rectangular grid. The analytical properties like convergence and stability of the rational cubic FIS are studied. Under some suitable hypotheses on the original function, the convergence of the rational cubic FIS is studied by calculating an upper bound for the uniform error of the surface interpolation. The stability results are studied when there is a small perturbation in the corresponding scaling factors. We also provide numerical examples to corroborate our theoretical results. - PublicationAffine zipper fractal interpolation functions(01-06-2020)
; ;Vijender, N. ;Viswanathan, P.Tetenov, A. V.This paper introduces a univariate interpolation scheme using a binary parameter called signature such that the graph of the interpolant—which we refer to as affine zipper fractal interpolation function—is obtained as an attractor of a suitable affine zipper. The scaling vector function is identified so that the graph of the corresponding affine zipper fractal interpolation function can be inscribed within a prescribed rectangle. Convergence analysis of the proposed affine zipper fractal interpolant is carried out. It is observed that for a fixed choice of discrete scaling factors, the box counting dimension of the graph of an affine zipper fractal interpolant is independent of the choice of a signature. Several examples of affine zipper fractal interpolants are presented to supplement our theory. - PublicationConvexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces(01-07-2017)
; ;Vijender, N.Navascués, M. A.Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. - PublicationShape preservation of scientific data through rational fractal splines(01-01-2014)
; ;Vijender, N.Navascués, M. A.Fractal interpolation is a modern technique in approximation theory to fit and analyze scientific data. We develop a new class of C1- rational cubic fractal interpolation functions, where the associated iterated function system uses rational functions of the form (Formula presented.) where pi(x) and qi(x) are cubic polynomials involving two shape parameters. The rational cubic iterated function system scheme provides an additional freedom over the classical rational cubic interpolants due to the presence of the scaling factors and shape parameters. The classical rational cubic functions are obtained as a special case of the developed fractal interpolants. An upper bound of the uniform error of the rational cubic fractal interpolation function with an original function in C2 is deduced for the convergence results. The rational fractal scheme is computationally economical, very much local, moderately local or global depending on the scaling factors and shape parameters. Appropriate restrictions on the scaling factors and shape parameters give sufficient conditions for a shape preserving rational cubic fractal interpolation function so that it is monotonic, positive, and convex if the data set is monotonic, positive, and convex, respectively. A visual illustration of the shape preserving fractal curves is provided to support our theoretical results. © 2013 Springer-Verlag Italia. - PublicationRational iterated function system for positive/monotonic shape preservation(01-01-2014)
; ;Vijender, N.Agarwal, R. P.In this paper we consider the (inverse) problem of determining the iterated function system (IFS) which produces a shaped fractal interpolant. We develop a new type of rational IFS by using functions of the form EiFi , where Ei are cubics and Fi are preassigned quadratics having 3-shape parameters. The fixed point of the developed rational cubic IFS is in C1, but its derivative varies from a piecewise differentiable function to a continuous nowhere differentiable function. An upper bound of the uniform error between the fixed point of a rational IFS and an original function φ ∈ C4 is deduced for the convergence results. The automatic generations of the scaling factors and shape parameters in the rational IFS are formulated so that its fixed point preserves the positive/monotonic features of prescribed data. The presence of scaling factors provides additional freedom to the shape of the fractal interpolant over its classical counterpart in the modeling of discrete data. © 2014 Chand et al.; licensee Springer.