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Splines in Numerical Integration

Udovičić, Zlatko (2010)

Mathematica Balkanica New Series

AMS Subj. Classification: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coefficients of the polynomials which correspond to the...

Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles

Josef Dalík (1999)

Archivum Mathematicum

An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple a 1 , , a 6 of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: a 1 , , a 6 are the vertices of triangles T 1 , , T 4 without obtuse inner angles such that T 1 has one side common with T j for j = 2 , 3 , 4 .

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