A New Approach to Trivariate Blending Rational Interpolation

2012 ◽  
Vol 546-547 ◽  
pp. 570-575 ◽  
Author(s):  
Le Zou ◽  
Jin Xie ◽  
Chang Wen Li
Keyword(s):  
Continued Fractions ◽  
Rational Interpolation ◽  
Interpolation Formula ◽  
Linear Interpolation ◽  
Interpolation Theorem ◽  
Newton Interpolation ◽  
New Approach ◽  
Barycentric Interpolation ◽  
Rational Interpolants ◽  
Data Pair

The advantages of barycentric interpolation formulations in computation are small number of floating points operations and good numerical stability. Adding a new data pair, the barycentric interpolation formula don’t require to renew computation of all basis functions. Thiele-type continued fractions interpolation and Newton interpolation may be the favoured nonlinear and linear interpolation. A new kind of trivariate blending rational interpolants were constructed by combining barycentric interpolation, Thiele continued fractions and Newton interpolation. We discussed the interpolation theorem, dual interpolation, no poles of the property and error estimation.

scholarly journals A New Approach to General Interpolation Formulae for Bivariate Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Le Zou ◽  
Shuo Tang
Keyword(s):  
Continued Fraction ◽  
Rational Interpolation ◽  
Interpolation Theorem ◽  
Interpolation Scheme ◽  
Bivariate Interpolation ◽  
New Approach ◽  
Multiple Parameters ◽  
Special Cases ◽  
Block Based ◽  
Branched Continued Fraction

General interpolation formulae for bivariate interpolation are established by introducing multiple parameters, which are extensions and improvements of those studied by Tan and Fang. The general interpolation formulae include general interpolation formulae of symmetric branched continued fraction, general interpolation formulae of univariate and bivariate interpolation, univariate block based blending rational interpolation, bivariate block based blending rational interpolation and their dual schemes, and some interpolation form studied by many scholars in recent years. We discuss the interpolation theorem, algorithms, dual interpolation, and special cases and give many kinds of interpolation scheme. Numerical examples are given to show the effectiveness of the method.

Fast Speed Expansion Technique for the Transient Analysis of Automotive Clutches

2004 ◽  
Author(s):  
Jiayin Li
Keyword(s):  
Large Scale ◽  
Expansion Method ◽  
Linear Interpolation ◽  
New Approach ◽  
Fast Speed ◽  
Transient Problem ◽  
Expansion Technique ◽  
Eigen Solutions ◽  
Modal Coordinates ◽  
Thermoelastic Contact Problem

The transient modal analysis method (TMA) has been used to solve the inhomogeneous (loaded) transient thermoelastic contact problem (ITTEC). In the TMA method, the solution of the inhomogeneous transient problem is expressed in modal coordinates, corresponding to eigenfunctions of the homogeneous (unloaded) problem. However, for the large-scale ITTEC problem, this method is found to be extremely time-consuming, because of the computation-intensive of the eigen-solutions. This paper describes a new approach to solve the large-scale ITTEC problem with a dramatic reduction in computational complexity. The method is referred to as fast speed expansion method (FSE). With the FSE method, full eigen-solutions are performed only at a limited number of sparsely located speeds. For speeds between these speeds, eigenvectors are solved by linear interpolation, while the eigenvalues are computed from Taylor series. The method is illustrated with application to an automotive clutches.

scholarly journals An Adaptive Image Inpainting Method Based on Continued Fractions Interpolation

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Lei He ◽  
Yan Xing ◽  
Kangxiong Xia ◽  
Jieqing Tan
Keyword(s):  
Continued Fractions ◽  
State Of The Art ◽  
Signal To Noise Ratio ◽  
Subjective Evaluation ◽  
Image Inpainting ◽  
Rational Interpolation ◽  
Objective Evaluation ◽  
Experimental Results ◽  
Signal To Noise

In view of the drawback of most image inpainting algorithms by which texture was not prominent, an adaptive inpainting algorithm based on continued fractions was proposed in this paper. In order to restore every damaged point, the information of known pixel points around the damaged point was used to interpolate the intensity of the damaged point. The proposed method included two steps; firstly, Thiele’s rational interpolation combined with the mask image was used to interpolate adaptively the intensities of damaged points to get an initial repaired image, and then Newton-Thiele’s rational interpolation was used to refine the initial repaired image to get a final result. In order to show the superiority of the proposed algorithm, plenty of experiments were tested on damaged images. Subjective evaluation and objective evaluation were used to evaluate the quality of repaired images, and the objective evaluation was comparison of Peak Signal to Noise Ratios (PSNRs). The experimental results showed that the proposed algorithm had better visual effect and higher Peak Signal to Noise Ratio compared with the state-of-the-art methods.

scholarly journals On a Bivariate Generalization of Berrut’s Barycentric Rational Interpolation to a Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2481
Author(s):  
Len Bos ◽  
Stefano De Marchi
Keyword(s):  
Rational Interpolation ◽  
Rational Interpolants ◽  
Barycentric Rational Interpolation

We discuss a generalization of Berrut’s first and second rational interpolants to the case of equally spaced points on a triangle in R2.

scholarly journals Heron’s cubic root iteration method with a new approach

2021 ◽  
Author(s):  
S. Gadtia ◽  
S. K. Padhan
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Interpolation Formula ◽  
Alternative Proof ◽  
New Approach ◽  
Iteration Formula ◽  
Odd Order ◽  
Even Order ◽  
Lagrange’S Method

Abstract Heron’s cubic root iteration formula conjectured by Wertheim is proved and extended for any odd order roots. Some possible proofs are suggested for the roots of even order. An alternative proof of Heron’s general cubic root iterative method is explained. Further, Lagrange’s interpolation formula for nth root of a number is studied and found that Al-Samawal’s and Lagrange’s method are equivalent. Again, counterexamples are discussed to justify the effectiveness of the present investigations.

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