Some Numerical Experiments in the Theory of Polynomial Interpolation

1965 ◽  
Vol 9 (3) ◽  
pp. 187-191 ◽  
Author(s):  
F. W. Luttmann ◽  
T. J. Rivlin
Keyword(s):  
Numerical Experiments ◽  
Polynomial Interpolation

scholarly journals On a Fast Convergence of the Rational-Trigonometric-Polynomial Interpolation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Arnak Poghosyan
Keyword(s):  
Trigonometric Polynomial ◽  
Numerical Experiments ◽  
Polynomial Interpolation ◽  
Convergence Acceleration ◽  
Fast Convergence ◽  
Exact Constants

We consider the convergence acceleration of the Krylov-Lanczos interpolation by rational correction functions and investigate convergence of the resultant parametric rational-trigonometric-polynomial interpolation. Exact constants of asymptotic errors are obtained in the regions away from discontinuities, and fast convergence of the rational-trigonometric-polynomial interpolation compared to the Krylov-Lanczos interpolation is observed. Results of numerical experiments confirm theoretical estimates and show how the parameters of the interpolations can be determined in practice.

scholarly journals A new approach for constructing mock-Chebyshev grids

2021 ◽  
Author(s):  
Ali IBRAHIMOGLU
Keyword(s):  
Numerical Experiments ◽  
Polynomial Interpolation ◽  
Numerical Results ◽  
Uniform Grid ◽  
New Approach ◽  
Chebyshev Nodes ◽  
Chebyshev Points ◽  
Runge Phenomenon ◽  
Equidistant Nodes

Polynomial interpolation with equidistant nodes is notoriously unreliable due to the Runge phenomenon, and is also numerically ill-conditioned. By taking advantage of the optimality of the interpolation processes on Chebyshev nodes, one of the best strategies to defeat the Runge phenomenon is to use the mock-Chebyshev points, which are selected from a satisfactory uniform grid, for polynomial interpolation. Yet, little literature exists on the computation of these points. In this study, we investigate the properties of the mock-Chebyshev nodes and propose a subsetting method for constructing mock-Chebyshev grids. Moreover, we provide a precise formula for the cardinality of a satisfactory uniform grid. Some numerical experiments using the points obtained by the method are given to show the effectiveness of the proposed method and numerical results are also provided.

scholarly journals Application Local Polynomial and Non-polynomial Splines of the Third Order of Approximation for the Construction of the Numerical Solution of the Volterra Integral Equation of the Second Kind

2021 ◽  
Vol 20 ◽  
Author(s):  
I. G. Burova
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Volterra Integral Equation ◽  
Numerical Experiments ◽  
Polynomial Interpolation ◽  
Order Of Approximation ◽  
Polynomial Splines ◽  
Third Order ◽  
The Third ◽  
Local Polynomial

The present paper is devoted to the application of local polynomial and non-polynomial interpolation splines of the third order of approximation for the numerical solution of the Volterra integral equation of the second kind. Computational schemes based on the use of the splines include the ability to calculate the integrals over the kernel multiplied by the basis function which are present in the computational methods. The application of polynomial and nonpolynomial splines to the solution of nonlinear Volterra integral equations is also discussed. The results of the numerical experiments are presented.

Controllable Compliance Joint For Human Oriented Robots

2013 ◽  
Vol 43 (1) ◽  
pp. 47-60
Author(s):  
Mihail Tsveov ◽  
Dimitar Chakarov
Keyword(s):  
Numerical Experiments ◽  
Position Control ◽  
Joint Stiffness ◽  
Joint Motion ◽  
Compliance Control ◽  
Leaf Springs ◽  
Antagonistic Actuation

Abstract In the paper, different approaches for compliance control for human oriented robots are revealed. The approaches based on the non- antagonistic and antagonistic actuation are compared. In addition, an approach is investigated in this work for the compliance and the position control in the joint by means of antagonistic actuation. It is based on the capability of the joint with torsion leaf springs to adjust its stiffness. Models of joint stiffness are presented in this paper with antagonistic and non-antagonistic influence of the spring forces on the joint motion. The stiffness and the position control possibilities are investigated and the opportunity for their decoupling as well. Some results of numerical experiments are presented in the paper too.

A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

2014 ◽  
Vol 8 (1) ◽  
pp. 218-221 ◽  
Author(s):  
Ping Hu ◽  
Zong-yao Wang
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Combination ◽  
Combination Rule ◽  
Combination Technique ◽  
Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

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