Journal ArticleDOI
A new class of rational cubic spline fractal interpolation function and its constrained aspects
Reads0
Chats0
TLDR
This paper constructs a new class of rational cubic spline FIFs (RCSFIFs) with a preassigned quadratic denominator with two shape parameters, which includes classical rational cubic interpolant [Appl. Comp., 216 (2010), pp. 2036–2049] as special case and improves the sufficient conditions for positivity.About:
This article is published in Applied Mathematics and Computation.The article was published on 2019-04-01. It has received 18 citations till now. The article focuses on the topics: Interpolation & Piecewise.read more
Citations
More filters
Journal ArticleDOI
Fractal Calculus on Fractal Interpolation Functions
TL;DR: In this paper, the Fα-calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non-differentiable and non-integrable in the sense of ordinary calculus.
Journal ArticleDOI
Shape preserving rational quartic fractal functions
TL;DR: The appearance of fractal interpolation function represents a revival of experimental mathematics, raised by computers and intensified by powerful evidence of its applications as mentioned in this paper, and it represents a new direction for experimental mathematics.
Journal ArticleDOI
Shape preserving rational cubic trigonometric fractal interpolation functions
TL;DR: A new family of C 1 -rational cubic trigonometric fractal interpolation functions (RCTFIFs) that are the generalized fractal version of the classical rational cubic trig onometric polynomial spline of the form p i ( θ ) ∕ q i (θ ) , where p i and q i are cubic trigonal polynomials with four shape parameters in each sub-interval.
Journal ArticleDOI
Multivariate Affine Fractal Interpolation
TL;DR: Fractal interpolation functions capture the irregularity of some data very effectively in comparison with the classical interpolants as discussed by the authors, and yield a new technique for fitting experimental data sample.
Journal ArticleDOI
Construction of cubic spline hidden variable recurrent fractal interpolation function and its fractional calculus
TL;DR: In this paper, a cubic spline hidden variable recurrent fractal interpolation function (CSHVRFIF) is constructed and its Riemann-Liouville fractional integral and derivative are also HRLFIFs.
References
More filters
Journal ArticleDOI
Monotone Piecewise Cubic Interpolation
F. N. Fritsch,R. E. Carlson +1 more
TL;DR: In this article, a monotone piecewise bicubic interpolation algorithm was proposed for data on a rectangular mesh, where the first partial derivatives and first mixed partial derivatives are determined by the mesh points.
Journal ArticleDOI
Fractal Functions and Interpolation
TL;DR: In this article, the authors introduce iterated function systems whose attractorsG are graphs of continuous functionsf∶I→R, which interpolate the data according tof(x��i)=y fixmei fori e {0,1,⋯,N}.
Journal ArticleDOI
The calculus of fractal interpolation functions
TL;DR: The calculus of deterministic fractal functions is introduced in this article, which can be explicitly indefinitely integrated any number of times, yielding a hierarchy of successively smoother interpolation functions which generalize splines and which are attractors for iterated function systems.
Journal ArticleDOI
Piecewise rational quadratic interpolation to monotonic data
J. A. Gregory,R. Delbourgo +1 more
TL;DR: In this paper, an explicit representation of a piecewise rational quadratic function is developed which produces a monotonic interpolant to given monotonicity data. But this method is not suitable for the case of complex data.
Journal ArticleDOI
Positivity of cubic polynomials on intervals and positive spline interpolation
Jochen W. Schmidt,Walter Heb +1 more
TL;DR: In this paper, a criterion for the positivity of a cubic polynomial on a given interval is derived, and a necessary and sufficient condition is given under which cubicC 1-spline interpolants are nonnegative.