Piecewise-polynomial (spline) interpolation

1967 ◽  
Vol 1 (1) ◽  
pp. 41-45 ◽  
Author(s):  
Yu. N. Subbotin
Keyword(s):  
Spline Interpolation ◽  
Polynomial Spline ◽  
Piecewise Polynomial

Solvability of cardinal spline interpolation problems

1983 ◽  
Vol 95 (1-2) ◽  
pp. 39-57
Author(s):  
T. N. T. Goodman
Keyword(s):  
Incidence Matrix ◽  
Bounded Solution ◽  
Spline Interpolation ◽  
Piecewise Polynomial ◽  
Piecewise Polynomials ◽  
Cardinal Spline ◽  
Interpolation Problems ◽  
Bounded Data ◽  
Derivatives Of ◽  
Cardinal Spline Interpolation

SynopsisWe consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points of a periodic vector x, specified by a periodic incidence matrix G. Similarly, we allow discontinuity of certain derivatives of the piecewise polynomial at certain points of x, specified by a periodic incidence matrix H. This generalises the well-known cardinal spline interpolation of Schoenberg. We investigate conditions on G, H and x under which there is a unique bounded solution for any given bounded data.

scholarly journals Optimum regular local spline interpolation of signals

2016 ◽  
pp. 24-31
Author(s):  
V. N. Isakov
Keyword(s):  
Spline Interpolation ◽  
Polynomial Spline ◽  
Optimal Interpolation ◽  
Optimum Approach ◽  
Local Spline ◽  
Special Case ◽  
Signal Interpolation

The study deals with an optimum approach to regular local signal interpolation by means of generalised splines. For the special case of local regular polynomial spline interpolation we derive quasi-optimal interpolation bases and provide corresponding recommendations dealing with selecting interpolation order and order of smoothness.

Lebesgue Constants for Cardinal -Spline Interpolation

1977 ◽  
Vol 29 (2) ◽  
pp. 441-448 ◽  
Author(s):  
J. Tzimbalario
Keyword(s):  
Differential Operator ◽  
Null Space ◽  
Spline Interpolation ◽  
Polynomial Spline ◽  
Lebesgue Constants ◽  
Real Zeros ◽  
Cardinal Spline ◽  
Image Position ◽  
Cardinal Spline Interpolation

Recently the theory of cardinal polynomial spline interpolation was extended to cardinals -splines [3]. Letbe a polynomial with only real zeros. Denote the set of zeros by . If is the associated differential operator, the null-space

Polynomial spline interpolation of incompatible boundary conditions with a single degenerate surface

2014 ◽  
Vol 53 ◽  
pp. 28-35
Author(s):  
Kan-Le Shi ◽  
Jun-Hai Yong ◽  
Yang Lu ◽  
Jia-Guang Sun ◽  
Jean-Claude Paul
Keyword(s):  
Boundary Conditions ◽  
Spline Interpolation ◽  
Polynomial Spline
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