STABILITY OF QUADRATIC INTERPOLATION POLYNOMIALS IN VERTICES OF TRIANGLES WITHOUT OBTUSE ANGLES

Josef Dalík

Address. Department of Mathematics, Technical University of Brno, Zizkova 17, 602 00 Brno, CZECH REPUBLIC

E-mail: mddal@fce.vutbr.cz

Abstract. An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple $a^1,\dots ,a^6$ of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: $a^1,\dots ,a^6$ are the vertices of triangles $T_1,\dots ,T_4$ without obtuse inner angles such that $T_1$ has one side common with $T_j$ for $j=2,3,4$.

AMSclassification. 65D05

Keywords. Quadratic Lagrange interpolation in 2D, stability