Stability of spline approximation methods for multidimensional pseudodifferential operators

1994 ◽  
Vol 19 (1) ◽  
pp. 25-64 ◽  
Author(s):  
R. Hagen ◽  
S. Roch ◽  
B. Silbermann
Keyword(s):  
Pseudodifferential Operators ◽  
Spline Approximation ◽  
Approximation Methods

scholarly journals Local spline approximation methods

1975 ◽  
Vol 15 (4) ◽  
pp. 294-325 ◽  
Author(s):  
Tom Lyche ◽  
Larry L Schumaker
Keyword(s):  
Spline Approximation ◽  
Approximation Methods ◽  
Local Spline

SPLINE APPROXIMATION APPLICATION TO RECONSTRUCTION OF DISCRETE MAP FUNCTIONS

2007 ◽  
Vol 17 (10) ◽  
pp. 3663-3667
Author(s):  
MARIA TOMASHEVSKAYA
Keyword(s):  
Time Series ◽  
Polynomial Approximation ◽  
Additive Noise ◽  
A Priori ◽  
Spline Approximation ◽  
Chaotic Time Series ◽  
Approximation Methods ◽  
Tent Map ◽  
Final Goal ◽  
Discrete Map

The final goal of conducted research is to make a comparison of spline and polynomial approximation methods to reconstruct a priori unknown nonlinear map functions based on observed chaotic time series in the additive noise presence. Logistic and tent map functions are considered in detail as an example.

scholarly journals Some multidimensional spline approximation methods

1974 ◽  
Vol 10 (1) ◽  
pp. 23-40 ◽  
Author(s):  
M.J Munteanu ◽  
L.L Schumaker
Keyword(s):  
Spline Approximation ◽  
Approximation Methods

A Voronovskaya Theorem for Variation-Diminishing Spline Approximation

1986 ◽  
Vol 38 (5) ◽  
pp. 1081-1093 ◽  
Author(s):  
M. J. Marsden
Keyword(s):  
Spline Function ◽  
Spline Approximation ◽  
Precise Definition ◽  
Approximation Methods ◽  
Real Numbers ◽  
Variation Diminishing ◽  
Definition Of ◽  
Image Position ◽  
Voronovskaya Theorem

In [7] Schoenberg introduced the following variation-diminishing spline approximation methods.Let m > 1 be an integer and let Δ = {xi} be a biinfinite sequence of real numbers with xi ≧ xi + l < xi+m. To a function f associate the spline function Vf of order m with knots Δ defined by(1.1)whereand the Nj(x) are B-splines with support xj < x < xj+m normalized so that ΣjNj(x) = 1. See, e.g., [2] for a precise definition of the Nj(x) and a discussion of the properties of Vf.

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