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Interpolation by Spline Functions
1993Even an elementary study of the interpolation problem $$s\left( {{t_i}} \right) = {f_i},\quad i = 0,...,n + 1 $$ in the simplest linear case, i.e., when s ∈ S 1(x 1,... ,x n ), shows that the solvability of the corresponding system depends entirely on the mutual location of the interpolation nodes \(t = \left\{ {{t_i}} \right\}_0^{n + 1}\) and ...
B. D. Bojanov +2 more
openaire +1 more source
1993
The spline function s(x) of odd degree 2r- 1 with knots x 1,..., x n is said to be a natural spline function, if the restriction of s over (-∞, x 1)and (x n , ∞) is a polynomial from π r-1. We shall denote by N 2r - 1(x 1,..., x n ) the class of natural spline functions of degree 2r - 1 with knots \(\left\{ {{x_k}} \right\}_1^n\). It is clear that N 2r
B. D. Bojanov +2 more
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The spline function s(x) of odd degree 2r- 1 with knots x 1,..., x n is said to be a natural spline function, if the restriction of s over (-∞, x 1)and (x n , ∞) is a polynomial from π r-1. We shall denote by N 2r - 1(x 1,..., x n ) the class of natural spline functions of degree 2r - 1 with knots \(\left\{ {{x_k}} \right\}_1^n\). It is clear that N 2r
B. D. Bojanov +2 more
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Reproducing kernel functions based univariate spline interpolation
Applied Mathematics Letters, 2021Fazhan Geng, Xinyuan Wu
exaly
2001
The refinement partition techniques are very effective in finite element methods and computer-aided geometric designs. However, the introduction of refinement partition may cause some inconvenience. We will discuss rational spline functions, especially the theory and methods of locally supported bivariate rational spline functions.
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The refinement partition techniques are very effective in finite element methods and computer-aided geometric designs. However, the introduction of refinement partition may cause some inconvenience. We will discuss rational spline functions, especially the theory and methods of locally supported bivariate rational spline functions.
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Interpolation with Spline Functions
2023Abdelwahab Kharab, Ronald B. Guenther
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