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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...
The paper has been presented at the 12th International Conference on Applications of
Computer Algebra, Varna, Bulgaria, June, 2006.To get guaranteed machine enclosures of a special function f(x),
an upper bound ε(f) of the relative error is needed, where ε(f) itself depends
on the error bounds ε(app); ε(eval) of the approximation and evaluation error
respectively. The approximation function g(x) ≈ f(x) is a rational function
(Remez algorithm), and with sufficiently high polynomial degrees ε(app)
becomes...
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