Now showing 1 - 5 of 5
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    Distribution of Noise in Linear Recurrent Fractal Interpolation Functions for Data Sets with α -Stable Noise
    In this study, we construct a linear recurrent fractal interpolation function (RFIF) with variable scaling parameters for data set with α -stable noise (a generalization of Gaussian noise) on its ordinate, which captures the uncertainty at any missing or unknown intermediate point. The propagation of uncertainty in this linear RFIF is investigated, and a method for estimating parameters of the uncertainty at any interpolated value is provided. Moreover, a simulation study to visualize uncertainty for interpolated values is presented.
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    Linear fractal interpolation function for data set with random noise
    Fractal interpolation is a contemporary technique to approximate numerous scientific experiments and natural phenomena. For data sets in 2, the simplest and easy-to-handle fractal interpolation functions (FIFs) are linear. In this study, we estimate probability distributions of linear FIFs for data sets with various types of random noise. In order to evaluate the distribution of any linear FIF associated with a prescribed data set having Student's t-distributed noise, we develop a technique to approximate the distribution of a linear combination of independent generalized Student's t-distributed random variables. In addition, we provide some statistical properties and numerical approximations of these linear fractal functions.
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    DISTRIBUTION of LINEAR FRACTAL INTERPOLATION FUNCTION for RANDOM DATASET with STABLE NOISE
    In this paper, we derive the probability distribution of linear fractal interpolation function (FIF) for a random dataset on R2, where randomness in the data is induced, using α-stable noise, in the second coordinate. In particular, we show that the distribution of linear FIF, at any point (on the first coordinate), is also stable, but with different parameters which can be estimated. Finally, we also provide statistical validity of our results.
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    Publication
    Linear Recurrent Fractal Interpolation Function for Data Set with Gaussian Noise
    In this article, we use the linear recurrent fractal interpolation function approach to interpolate a data set with Gaussian noise on its ordinate. To investigate the variability at any intermediate point in the given noisy data set, we estimate the parameters of the probability distribution of the fractal function. In addition, we present a simulation study that experimentally confirms our theoretical findings.
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    Publication
    Zipper rational fractal interpolation functions
    (2024-01-01)
    Pasupathi, R.
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    A classical piecewise interpolant can be redefined by utilizing horizontal contractive maps that project the entire domain onto subintervals, ensuring uniqueness. By applying the concept of a zipper, this traditional spline approach is expanded into a broader category of piecewise interpolants through the use of a binary vector signature. In particular, we extend rational spline with cubic/quadratic functions with shape parameters to generate a new class of zipper rational interpolants. Further, we fractalize these interpolants to generate zipper rational cubic α-fractal functions. It is demonstrated that the proposed interpolants achieve uniform convergence to a C1-data generating function. We establish appropriate constraints on shape parameters, vertical scalings, and signatures to ensure the creation of shape-preserving zipper rational cubic splines and zipper rational cubic α-fractal functions. These theoretical results are substantiated with carefully selected numerical examples.