Proposal for Use the Fractional Derivative of Radial Functions in Interpolation Problems
arXiv:1906.03760 · doi:10.3390/fractalfract8010016
Abstract
In this document we present the construction of a radial functions that have the objective of emulating the behavior of the radial basis function thin plate spline (TPS), which we will name as function TPS, we propose a way to partially and totally apply the fractional derivative to these functions to be used in interpolation problems, a proposal is presented to precondition the matrices generated in the interpolation problem using the decomposition and finally is proposed the form of a radial interpolant to be used when solving differential equations using the asymmetric collocation method.
References in corpus (11)
- A Caputo fractional derivative of a function with respect to another function
- A Generalized Definition of Fractional Derivative with Applications
- Radial Basis Function Networks for Convolutional Neural Networks to Learn Similarity Distance Metric and Improve Interpretability
- Fractional Newton-Raphson Method Accelerated with Aitken's Method
- Fractional Newton-Raphson Method
- An approximation to zeros of the Riemann zeta function using fractional calculus
- Introducción al Cálculo Fraccional
- Sets of fractional operators and numerical estimation of the order of convergence of a family of fractional fixed point methods
- Reduction of a nonlinear system and its numerical solution using a fractional iterative method
- Acceleration of the order of convergence of a family of fractional fixed point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers
- Fractional Newton-Raphson Method and Some Variants for the Solution of Non-linear Systems