منابع مشابه
On Convergent Interpolatory Subdivision Schemes in Riemannian Geometry
We show the convergence (for all input data) of refinement rules in Riemannian manifolds which are analogous to the linear four-point scheme and similar univariate interpolatory schemes, and which are generalized to the Riemannian setting by the so-called log/exp analogy. For this purpose we use a lemma on the Hölder regularity of limits of contractive refinement schemes in metric spaces. In co...
متن کاملPositive interpolatory quadrature rules generated by some biorthogonal polynomials
Interpolatory quadrature rules whose abscissas are zeros of a biorthogonal polynomial have proved to be useful, especially in numerical integration of singular integrands. However, the positivity of their weights has remained an open question, in some cases, since 1980. We present a general criterion for this positivity. As a consequence, we establish positivity of the weights in a quadrature r...
متن کاملA New Class of Non-stationary Interpolatory Subdivision Schemes Based on Exponential Polynomials
We present a new class of non-stationary, interpolatory subdivision schemes that can exactly reconstruct parametric surfaces including exponential polynomials. The subdivision rules in our scheme are interpolatory and are obtained using the property of reproducing exponential polynomials which constitute a shift-invariant space. It enables our scheme to exactly reproduce rotational features in ...
متن کاملOn the Almost Everywhere Divergence of Lagrange Interpolatory Polynomials for Arbitrary System of Nodes
are the Lebesgue functions and Lebesgue constants of the interpolation, respectively . We now prove this statement in full detail . The detailed proof turned out to be quite complicated and several unsuspected difficulties had to be overcome . In the same paper P. Erdős also stated, that there is a pointgroup {x kn } so that for every continuous f (x) (-1 x:1) L,,(f, x,) -f (xo) holds for at le...
متن کاملAnalysis of Non-stationary Interpolatory Subdivision Schemes Based on Exponential Polynomials
In this study, we are concerned with non-stationary interpolatory subdivision schemes with refinement rules which may vary from level to level. First, we derive a new class of interpolatory non-stationary subdivision schemes reproducing exponential polynomials. Next, we prove that non-stationary schemes based on the known butterfly-shaped stencils possess the same smoothness as the known Butter...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1989
ISSN: 0021-9045
DOI: 10.1016/0021-9045(89)90022-1