منابع مشابه
Monotone Rational Trigonometric Interpolation
This study is concerned with the visualization of monotone data using a piecewise C rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free. Figures are used widely to exhibit that the pr...
متن کاملThree-monotone interpolation
A function f : R → R is called k-monotone if it is (k − 2)-times differentiable and its (k − 2)nd derivative is convex. A point set P ⊂ R is k-monotone interpolable if it lies on a graph of a k-monotone function. These notions have been studied in analysis, approximation theory etc. since the 1940s. We show that 3-monotone interpolability is very non-local: we exhibit an arbitrarily large finit...
متن کاملOn 3-monotone approximation by piecewise polynomials
Abstract. We consider 3-monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3-monotone uniform approximation of a 3-monotone function, to convex local L1 approximation of the derivative of the function. As the corollary we obtain Jackson-type estimates on the degree of 3-monotone approximation by piecewise polynomials ...
متن کاملUniform Interpolation for Monotone Modal Logic
We reconstruct the syntax and semantics of monotone modal logic, in the style of Moss’ coalgebraic logic. To that aim, we replace the box and diamond with a modality ∇ which takes a finite collection of finite sets of formulas as its argument. The semantics of this modality in monotone neighborhood models is defined in terms of a version of relation lifting that is appropriate for this setting....
متن کاملOn Monotone and Convex Spline Interpolation*
This paper is concerned with the problem of existence of monotone and/or convex splines, having degree n and order of continuity k, which interpolate to a set of data at the knots. The interpolating splines are obtained by using Bernstein polynomials of suitable continuous piecewise linear functions; they satisfy the inequality k < n — k. The theorems presented here are useful in developing alg...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1977
ISSN: 0021-9045
DOI: 10.1016/0021-9045(77)90011-9