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Cardinal B-spline dictionaries on a compact interval [PDF]

Applied and Computational Harmonic Analysis, 2005
A prescription for constructing dictionaries for cardinal spline spaces on a compact interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the
Laura Rebollo-Neira
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A Class of Cardinal Trigonometric Splines

SIAM Journal on Mathematical Analysis, 1976
About a decade ago Schoenberg introduced trigonometric splines which are related to the differential operator $\Delta m = D(D^2 + 1^2 ) \cdots (D^2 + m^2 )$. Here we introduce the cardinal trigonometric splines and show that cardinal trigonometric interpolation at the nodes to data of power growth is not unique.
Sharma, A., Tzimbalario, J.
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On the convergence of cardinal splines

Applied and Computational Harmonic Analysis, 2020
Abstract This note contains an outline of a solution to the following conjecture formulated by I. J. Schoenberg in 1976: If the function f is in the Bernstein class B π and S k ( { f ( n ) } , x ) is the piecewise polynomial cardinal spline of order 2k that interpolates ( n , f ( n ) ) , n = 0 , ±
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Cardinal hermite interpolation with box splines

Constructive Approximation, 1987
The authors initiate a study of multivariate cardinal Hermite interpolation: the interpolation of successive directional derivatives. It is assumed that the set T of directions satisfies a certain determinant condition and that each direction t occurs in T with even multiplicity.
Riemenschneider, Sherman, Scherer, Karl
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On Cardinal Spline Smoothing

1979
Publisher Summary The chapter describes the methods, with some changes, that were used by the author to solve the numerical problem assigned to him at the Ballistics Research Laboratories in Aberdeen, Maryland, during the Second World War. The problem was to smooth very extended equidistant tables of drag functions (or drag coefficients) by ...
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On minimax cardinal spline interpolation

Statistical Inference for Stochastic Processes, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Elementarym-harmonic cardinal B-splines

Numerical Algorithms, 1992
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Spline Functions on the Circle: Cardinal L-Splines Revisited

Canadian Journal of Mathematics, 1980
Although the literature on splines has grown vastly during the last decade [11], the study of polynomial splines on the circle seems to have suffered neglect. The first to study the subject in depth seem to be Ahlberg, Nilson and Walsh [1]. Almost at the same time I. J.
Micchelli, Charles A., Sharma, A.
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Cardinal Interpolation and Spline Functions VII. the Behavior of Cardinal Spline Interpolants as their Degree Tends to Infinity

Journal d'Analyse Mathématique, 1974
Let F(x) be a function from ℝ to ℂ and let $$S_m \left( x \right)\, = \,\sum\limits_{ - \infty }^\infty {F\left( \nu \right)L_m \left( {x - \nu } \right)}$$ (1) be the spline function of degree 2m−1, with knots at the integers, that interpolates F(x) at all the integers.
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On the Cardinal Spline Interpolant to $e^{iut} $

SIAM Journal on Mathematical Analysis, 1976
The cardinal spline interpolant $S_{n,u} $ of degree n to $\exp (iut)$ is shown to satisfy $| {S_{n,u} (t)} | < 1$ unless t is an interpolation point. Also, it is shown that $1 < C_n *#60; 1 + 2^{1 - n} $ for all odd n and $C_n = 1$ for all positive even n, with $C_n: = \sup _{u,t} {{ |\exp (iut) - S_{n,u} (t) |} / {| {u / \pi }} |^{n + 1} }$
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