Minimizing the quasi-interpolation error for bivariate discrete quasi-interpolants

We define a class of discrete quasi-interpolants based on bivariate box splines by imposing the exactness on a space of polynomials of total degree, depending on the box spline and minimizing a constant appearing in the leading term of an appropriate quasi-interpolation error estimate. We give some...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 224; no. 1; pp. 250 - 268
Main Authors Barrera-Rosillo, Domingo, Ibáñez-Pérez, María José
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 01.02.2009
Elsevier
Subjects
Approximations and expansions
Best uniform approximation
Box splines
Discrete quasi-interpolants
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Quasi-interpolation error
Sciences and techniques of general use
Best uniform approximation
Quasi-interpolation error
Box splines
Discrete quasi-interpolants
Polynomial
Error estimation
Uniform approximation
Spline approximation
Numerical approximation
Interpolation
Numerical analysis
Applied mathematics
Best approximation
Bivariate spline
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Summary:We define a class of discrete quasi-interpolants based on bivariate box splines by imposing the exactness on a space of polynomials of total degree, depending on the box spline and minimizing a constant appearing in the leading term of an appropriate quasi-interpolation error estimate. We give some C 1 quadratic and C 2 quartic examples and compare them with other well-known quasi-interpolants.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2008.05.005