scholarly journals The Lebesgue constants for some cardinal spline interpolation operators

1982 ◽  
Vol 36 (2) ◽  
pp. 104-118 ◽  
Author(s):  
T.N.T Goodman
Keyword(s):  
Spline Interpolation ◽  
Lebesgue Constants ◽  
Cardinal Spline ◽  
Interpolation Operators ◽  
Cardinal Spline Interpolation

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

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.

On Cardinal Spline Interpolation

2013 ◽  
Vol 13 (1) ◽  
pp. 39-54
Author(s):  
Rolf D. Grigorieff
Keyword(s):  
Unique Solution ◽  
Error Estimates ◽  
Interpolation Problem ◽  
Polynomial Growth ◽  
Spline Interpolation ◽  
Cardinal Spline ◽  
Cardinal Splines ◽  
Cardinal Spline Interpolation

Abstract. In the present paper it is shown that the interpolation problem for multiple knot cardinal splines subject to general interpolation conditions has a unique solution with polynomial growth if the data grow correspondingly provided a certain determinantal condition is satisfied. An application to Hs error estimates for the interpolation with periodic multiple knot splines is given.

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