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

Josef Dalík

Displaying similar documents to “Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles”

Additive groups connected with asymptotic stability of some differential equations

Árpád Elbert (1998)

Archivum Mathematicum

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The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient $λ^{2} q (s), s \in [s_{0}, \infty)$ is investigated, where $λ \in ℝ$ and $q (s)$ is a nondecreasing step function tending to $\infty$ as $s \to \infty$ . Let $S$ denote the set of those $λ$ ’s for which the corresponding differential equation has a solution not tending to 0. It is proved that $S$ is an additive group. Four examples are given with $S = {0}$ , $S = ℤ$ , $S = 𝔻$ (i.e. the set of dyadic numbers), and $ℚ \subset S ⫋ ℝ$ .

An inequality for the coefficients of a cosine polynomial

Horst Alzer (1995)

Commentationes Mathematicae Universitatis Carolinae

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We prove: If $\frac{1}{2} + \sum_{k = 1}^{n} a_{k} (n) cos (k x) \geq 0 for all x \in [0, 2 π),$ then $1 - a_{k} (n) \geq \frac{1}{2} \frac{k^{2}}{n^{2}} for k = 1, \dots, n .$ The constant $1 / 2$ is the best possible.

Optimal-order quadratic interpolation in vertices of unstructured triangulations

Josef Dalík (2008)

Applications of Mathematics

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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...