Fast and stable computation of the barycentric representation of rational interpolants

CALCOLO ◽  
1996 ◽  
Vol 33 (3-4) ◽  
pp. 371-388 ◽  
Author(s):  
L. Gemignani
Keyword(s):  
Rational Interpolants ◽  
Stable Computation ◽  
Barycentric Representation

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

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.

Stable Computation of Hahn Moments for Large Size 1D Signal Analysis

2020 ◽  
pp. 95-102
Author(s):  
Achraf Daoui ◽  
Omar El Ogri ◽  
Mohamed Yamni ◽  
Hicham Karmouni ◽  
Mhamed Sayyouri ◽  
...  
Keyword(s):  
Signal Analysis ◽  
Large Size ◽  
Stable Computation

Partial 3D Image Reconstruction by Cuboids Using Stable Computation of Hahn Polynomials

2021 ◽  
pp. 831-842
Author(s):  
Mohamed Amine Tahiri ◽  
Hicham Karmouni ◽  
Ahmed Tahiri ◽  
Mhamed Sayyouri ◽  
Hassan Qjidaa
Keyword(s):  
Image Reconstruction ◽  
3D Image ◽  
3D Image Reconstruction ◽  
Hahn Polynomials ◽  
Stable Computation
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