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 The barycentric rational interpolation collocation method for boundary value problems

2018 ◽  
Vol 22 (4) ◽  
pp. 1773-1779 ◽  
Author(s):  
Dan Tian ◽  
Ji-Huan He
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Analytical Methods ◽  
Boundary Value ◽  
Rational Interpolation ◽  
Higher Order ◽  
Barycentric Rational Interpolation

Higher-order boundary value problems have been widely studied in thermal science, though there are some analytical methods available for such problems, the barycentric rational interpolation collocation method is proved in this paper to be the most effective as shown in three examples.

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 Convergence of Linear Barycentric Rational Interpolation for Analytic Functions

2012 ◽  
Vol 50 (5) ◽  
pp. 2560-2580 ◽  
Author(s):  
Stefan Güttel ◽  
Georges Klein
Keyword(s):  
Analytic Functions ◽  
Rational Interpolation ◽  
Barycentric Rational Interpolation

scholarly journals Linear Barycentric Rational Method for Solving Schrodinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Peichen Zhao ◽  
Yongling Cheng
Keyword(s):  
Schrödinger Equation ◽  
Convergence Rate ◽  
Collocation Method ◽  
Schrodinger Equation ◽  
Interpolation Method ◽  
Rational Interpolation ◽  
Barycentric Interpolation ◽  
Rational Polynomial ◽  
The Matrix ◽  
Barycentric Rational Interpolation

A linear barycentric rational collocation method (LBRCM) for solving Schrodinger equation (SDE) is proposed. According to the barycentric interpolation method (BIM) of rational polynomial and Chebyshev polynomial, the matrix form of the collocation method (CM) that is easy to program is obtained. The convergence rate of the LBRCM for solving the Schrodinger equation is proved from the convergence rate of linear barycentric rational interpolation. Finally, a numerical example verifies the correctness of the theoretical analysis.

scholarly journals A Bayesian approach to time-varying latent strengths in pairwise comparisons

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0251945
Author(s):  
Blaž Krese ◽  
Erik Štrumbelj
Keyword(s):  
Bayesian Approach ◽  
Gaussian Processes ◽  
Rational Interpolation ◽  
Pairwise Comparisons ◽  
Time Varying ◽  
Data Set ◽  
Additional Information ◽  
Time Component ◽  
Barycentric Rational Interpolation ◽  
Sports Data

The famous Bradley-Terry model for pairwise comparisons is widely used for ranking objects and is often applied to sports data. In this paper we extend the Bradley-Terry model by allowing time-varying latent strengths of compared objects. The time component is modelled with barycentric rational interpolation and Gaussian processes. We also allow for the inclusion of additional information in the form of outcome probabilities. Our models are evaluated and compared on toy data set and real sports data from ATP tennis matches and NBA games. We demonstrated that using Gaussian processes is advantageous compared to barycentric rational interpolation as they are more flexible to model discontinuities and are less sensitive to initial parameters settings. However, all investigated models proved to be robust to over-fitting and perform well with situations of volatile and of constant latent strengths. When using barycentric rational interpolation it has turned out that applying Bayesian approach gives better results than by using MLE. Performance of the models is further improved by incorporating the outcome probabilities.

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