Interpolation of operators
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Multivariate n-term rational and piecewise polynomial approximation
Journal of Approximation Theory
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We study nonlinear approximation in Lp(R2), 0 〈 p 〈 ∞, from n-term rational functions. Our main result relates n-term rational approxmation in Lp to nonlinear approximation from a broad class of piecewise polynomials over multilevel triangulations allowing a lot of flexibility and, in particular, arbitrarily sharp angles. This relationship and the existing estimates for spline approximation give a Jackson estimate for n-term rational approximation in terms of a minimal smoothness norm over a large collection of anisotropic Besov-type spaces (B-spaces).