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Multivariate simultaneous approximation

Constructive Approximation, 2002
Using convolution techniques, the Fourier transform, and complex analysis, theorems of Jackson type are given, for the simultaneous approximation of a function of class \(C^m\) and its partial derivatives, by a polynomial and the corresponding partial derivatives.
BAGBY T.   +2 more
exaly   +4 more sources

Simultaneous Polynomial Approximation

SIAM Journal on Mathematical Analysis, 1993
The authors prove the approximation theorem on simultaneous approximation of \(f\in C^ s[- 1,1]\) and its derivatives of order \(j\), \(0\leq j\leq s\), by polynomials of degree \(n\) and their derivatives which has filled the gap between Timan-Trigub's type theorem and the classical norm estimate of the Jackson type.
Ditzian, Z.   +2 more
openaire   +2 more sources

On simultaneous approximation

Numerical Functional Analysis and Optimization, 1998
In this exposition, we investigate in an extended framework the problem of simultaneous best approximation. Refinement of a formula for the subdifferential of restricted radius of a p-bounded set leads us to explore some interesting results on strong uniqueness of simultaneous best approximants. In particular, we also.
LAURENT, PJ, PAI, D
openaire   +2 more sources

Suitable Norms for Simultaneous Approximation

Acta Mathematica Hungarica, 1997
The most common way to study simultaneous approximation of two points \(x,y\) of a normed linear space \(E\) from a subset \(M\) of \(E\), is to consider a suitable norm in \(E\times E\) (for instance, \(\| (u,v)\| =\sup(\| u\| ,\| v\|)\), \(\| (u,v)\| =\| u\| +\| v\|)\) and to reduce this problem to the ordinary approximation of the single point \((x ...
Benítez, Carlos   +2 more
openaire   +3 more sources

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