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 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.

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 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.

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