2017
DOI: 10.1007/s00025-017-0682-8
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Rational Operators Based on q-Integers

Abstract: Shepard-type rational operators based on q−integers are studied and convergence results and pointwise approximation error estimates improving previous statements are obtained. Influence of choice of q on the error estimates is also discussed. Techniques in CAGD for shape modeling of rational curves based on above operators are also presented and numerical examples are given.

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Cited by 3 publications
(1 citation statement)
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“…The approximation behavior of operator is well known and direct and converse results, saturation statements and simultaneous approximation estimates not possible by polynomials and corresponding to several nodes meshes distributions can be found for example in [ 1 , 2 , 4 7 , 13 , 27 ]. Applications to scattered data interpolation problems, CAGD and image compression were also examined (see e.g.…”
Section: Resultsmentioning
confidence: 99%
“…The approximation behavior of operator is well known and direct and converse results, saturation statements and simultaneous approximation estimates not possible by polynomials and corresponding to several nodes meshes distributions can be found for example in [ 1 , 2 , 4 7 , 13 , 27 ]. Applications to scattered data interpolation problems, CAGD and image compression were also examined (see e.g.…”
Section: Resultsmentioning
confidence: 99%