Rational Interpolation and Its Ill-conditioned Property

2007 ◽  
pp. 47-53 ◽  
Author(s):  
Hiroshi Kai
Keyword(s):  
Rational Interpolation

Comonotone and coconvex rational interpolation and approximation

2011 ◽  
Vol 58 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Hoa Thang Nguyen ◽  
Annie Cuyt ◽  
Oliver Salazar Celis
Keyword(s):  
Rational Interpolation

scholarly journals Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinru Liu ◽  
Yuanpeng Zhu ◽  
Shengjun Liu
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Rectangular Domain ◽  
Interpolation Spline ◽  
Spline Surface ◽  
Surface Data ◽  
Shape Preserving Interpolation ◽  
The Given ◽  
Surface Construction ◽  
Special Case

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.

scholarly journals Shape-Preserving Rational Interpolation Scheme for Regular Surface Data

2015 ◽  
Vol 2 (4) ◽  
pp. 713-747
Author(s):  
Maria Hussain ◽  
Malik Zawwar Hussain ◽  
Muhammad Sarfraz
Keyword(s):  
Rational Interpolation ◽  
Interpolation Scheme ◽  
Shape Preserving ◽  
Regular Surface ◽  
Surface Data

scholarly journals Structured matrices and unconstrained rational interpolation problems

1994 ◽  
Vol 203-204 ◽  
pp. 155-188 ◽  
Author(s):  
Tibor Boros ◽  
Ali H. Sayed ◽  
Thomas Kailath
Keyword(s):  
Rational Interpolation ◽  
Structured Matrices ◽  
Interpolation Problems

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 Rational interpolation of the function |x|α by an extended system of Chebyshev – Markov nodes

2020 ◽  
Vol 55 (4) ◽  
pp. 391-405
Author(s):  
E. A. Rovba ◽  
V. Yu. Medvedeva
Keyword(s):  
Rational Functions ◽  
Rational Interpolation ◽  
Asymptotic Equality ◽  
Fixed Number ◽  
Theoretical Research ◽  
Extended System ◽  
Uniform Approximations ◽  
Upper Estimate ◽  
Interpolation Functions ◽  
Interpolation Nodes

In this paper, we study the approximations of a function |x|α, α > 0 by interpolation rational Lagrange functions on a segment [–1,1]. The zeros of the even Chebyshev – Markov rational functions and a point x = 0 are chosen as the interpolation nodes. An integral representation of an interpolation remainder and an upper bound for the considered uniform approximations are obtained. Based on them, a detailed study is made:a) the polynomial case. Here, the authors come to the famous asymptotic equality of M. N. Hanzburg;b) at a fixed number of geometrically different poles, the upper estimate is obtained for the corresponding uniform approximations, which improves the well-known result of K. N. Lungu;c) when approximating by general Lagrange rational interpolation functions, the estimate of uniform approximations is found and it is shown that at the ends of the segment [–1,1] it can be improved.The results can be applied in theoretical research and numerical methods. 

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