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Segeth, Karel
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The paper is concerned with the approximation and interpolation employing polyharmonic splines in multivariate problems. The properties of approximants and interpolants based on these radial basis functions are shown. The methods of such data fitting are applied in practice to treat the problems of, e.g., geographic information systems, signal processing, etc. A simple 1D computational example is presented.
Segeth, Karel
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We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational...
Petr Luner, Jan Flusser (2005)
Kybernetika
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The paper deals with effective calculation of Thin-Plate Splines (TPS). We present a new modification of hierarchical approximation scheme. Unlike 2-D schemes published earlier, we propose an 1-D approximation. The new method yields lower computing complexity while it preserves the approximation accuracy.
Kurt Jetter, Joachim Stöckler (1991/92)
Numerische Mathematik
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S. I. Novikov (1989)
Banach Center Publications
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Wu, Jinming, Zhang, Xiaolei, Peng, Lihui (2010)
Mathematical Problems in Engineering
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W. Dahmen, T.N.T. Goodman (1987/88)
Numerische Mathematik
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Isaac J. Schoenberg (1967-1968)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Segeth, Karel
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There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known...
M.E.A. El Tom (1979)
Numerische Mathematik
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