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Here, we present an improved construction employing the cardinal function of the multiresolution.
The polynomial or trigonometric interpolant of an arbitrary function f(x) may be represented as a "cardinal function" series whose coefficients are the values of f(x) at the interpolation points.
where Card(x) is the cardinal function which returns the set size.
The method is based on approximating functions and their derivatives by using the Whittaker cardinal function.
Whenever the series in (2.7) converges, it is called the Whittaker cardinal function of f.
Then the Whittaker cardinal function is defined by the infinite series as follows: C f,h,x =sum_{j=-infty}^{infty}f(jh)S(j,x =sum_{j=-infty
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Among other things, we will give up the sentimental notion that one of the cardinal functions of education is to bring out the individual nature of every child.
One of these responses seems to be the activation of endogenous endonucleases, enzymes in the cell nucleus that "suicidally" disrupt its cardinal functions.
We show that the corresponding cardinal functions for a uniform, unbounded grid are all approximated by the same function: C X) ∼ (1/ sin (πX)/sinh (πX/ρ) for some constant ρ which depends on the inverse width parameter ("shape parameter") α of the RBF and also on the RBF species.
The other topics are the cardinal functions of primary care.
The basis of the interpolant will be defined by 12 cubic polynomial cardinal functions in each sub-triangle.
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