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Onesided approximation and real interpolation.

N. Krugljak, E. Matvejev (1997)

Collectanea Mathematica

It is proved that the reiteration theorem is not valid for the spaces Ap (theta,q) defined by V. Popov by means of onesided approximation. It is also proved that a class of cones, defined by onesided approximation of piecewise linear functions on the interval [0,1], is stable for the real interpolation method.

Optimal-order quadratic interpolation in vertices of unstructured triangulations

Josef Dalík (2008)

Applications of Mathematics

We study the problem of Lagrange interpolation of functions of two variables by quadratic polynomials under the condition that nodes of interpolation are vertices of a triangulation. For an extensive class of triangulations we prove that every inner vertex belongs to a local six-tuple of vertices which, used as nodes of interpolation, have the following property: For every smooth function there exists a unique quadratic Lagrange interpolation polynomial and the related local interpolation error...

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