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Interpolating polynomial wavelets on [?1,1]
Advances in Computational Mathematics, 2004The authors use a system of orthogonal polynomials with respect to the four Chebyshev weights, \(1/\sqrt(1-x^2)\), \(\sqrt(1-x^2)\), \(\sqrt{[(1-x)/(1+x)]}\) and \(\sqrt{[(1+x)/(1-x)]}\), with positive leading coefficients and Darboux kernels to construct four interpolating scaling functions and interpolating wavelets with a multiresolution structure ...
Capobianco MR, Themistoclakis W
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Lacunary Polynomial Spline Interpolation
SIAM Journal on Numerical Analysis, 1976A special form of the Birkhoff interpolation problem is investigated. We prove an existence theorem for certain types of interpolation which, in a particular case, reduces to a theorem of Meir and Sharma for $(0,2)$ interpolation by $C^3 $ piecewise quintics.
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C1 trivariate polynomial interpolation
Computer Aided Geometric Design, 1987By using monomial bases which triangularize the Vandermonde matrix, a trivariate polynomial of degree nine interpolating to data on a tetrahedron is constructed. This polynomial can be used to define a continuously differentiable piecewise function on an arbitrary triangulated domain in \(R^ 3\). An example was given to test the interpolant.
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