Bivariate Interpolation on the Hypersphere with Thiele Type Rational Interpolants

2014 ◽  
Vol 11 (11) ◽  
pp. 3873-3881
Author(s):  
Qiushi Wang
Keyword(s):  
Bivariate Interpolation ◽  
Rational Interpolants

On the approximation of $ \ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants

2019 ◽  
pp. 32-37
Author(s):  
Abdul-Rashid Ramazanov ◽  
V.G. Magomedova
Keyword(s):  
Convergence Rate ◽  
Spline Functions ◽  
Rational Spline ◽  
Rational Interpolants ◽  
Half Axis

For the function $f(x)=\exp(-x)$, $x\in [0,+\infty)$ on grids of nodes $\Delta: 0=x_0<x_1<\dots $ with $x_n\to +\infty$ we construct rational spline-functions such that $R_k(x,f, \Delta)=R_i(x,f)A_{i,k}(x)\linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $x\in[x_{i-1}, x_i]$ $(i=1,2,\dots)$ and $k=1,2,\dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=\alpha_j+\beta_j(x-x_j)+\gamma_j/(x+1)$ $(j=1,2,\dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)\equiv R_1(x,f)$. Bounds for the convergence rate of $R_k(x,f, \Delta)$ with $f(x)=\exp(-x)$, $x\in [0,+\infty)$, are found.

Splines on rational interpolants

2015 ◽  
pp. 21-30
Author(s):  
Abdul-Rashid Ramazanov ◽  
Vazipat Magomedova ◽  
◽  
Keyword(s):  
Rational Interpolants

Solvability problems of bivariate interpolation I

1986 ◽  
Vol 2 (1) ◽  
pp. 153-169 ◽  
Author(s):  
G. G. Lorentz ◽  
R. A. Lorentz
Keyword(s):  
Bivariate Interpolation

scholarly journals Perturbation of nodes and poles in certain rational interpolants

1987 ◽  
Vol 36 (2) ◽  
pp. 177-185
Author(s):  
M.A. Bokhari
Keyword(s):  
Rational Interpolants

Recently, E.B. Saff and A. Sharma proved a result on Walsh's type equiconvergence for certain sequences of rational interpolants having uniformly distributed poles and nodes of interpolation. Here we examine the sensitivity of this result to a slight perturbation of the poles and nodes. Some problems related to our work are also formulated.

Bivariate Interpolation with Quadratic Box Splines

1988 ◽  
Vol 51 (183) ◽  
pp. 219
Author(s):  
Morten Daehlen ◽  
Tom Lyche
Keyword(s):  
Box Splines ◽  
Bivariate Interpolation
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