A New Approximation Method with High Order Accuracy

Abstract

Abstract:In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and cubic B-spline quasi-interpolation operator. Error analysis shows that our method produces higher accuracy compared with other approaches. Numerical examples demonstrate that the proposed scheme is effective.

Comparative Numerical Solution of Fractional Spline with Continuity Equations

“…In this section, we'll look at the stability analysis of the proposed spline method. Equations (4), ( 5), (6), and (7) are considered for evaluating the equation's stability and providing a method to test it, using fractional differential equations, and is dedicated to the stability of the linear system by removing the effects of errors. ] 𝑆 𝑖−1 (2) ; (2)…”

“…Many known models are defined as none (fractional) order derivatives in diffusion processes, viscoelasticity, electrochemistry, and other fields. Some numerical algorithms for solving various derivatives of fractional order problems are [5] and [6]. One of the most useful techniques for the numerical approximation of functions is fractional order spline functions.…”

“…One of the most useful techniques for the numerical approximation of functions is fractional order spline functions. According to the researchers, other difficult [6] and [7] problems should be replaced by new work and projects. On one hand, there is a great method for the numerical approximation of functions using spline functions.…”

An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization

“…The NRBA trajectories are denoted NRBA 1 , NRBA 2 , and NRBA 3 and differ in the choice of R P . We use R P = 10 4 for NRBA 1 , R P = 500 for NRBA 2 , and R P = 100 for NRBA 3 . The remaining parameter values are R v = 5, R a = 10, R j = 1, I = 1,q L = 0.005,q N = 0.5,p = 15, P = 1000, ∆τ κ = 2, and ∆τ It = 0.25.…”

“…B-spline functions, curves, and surfaces are widely used for approximation [1][2][3] and for defining the trajectories of vehicles [4,5], robots [6,7] and industrial machines [8]. Furthermore, they are common in computer graphics [9,10] and signal processing for filter design and signal representation [11][12][13][14][15].…”