Markov-type inequalities and the degree of convex spline interpolation
نویسندگان
چکیده
منابع مشابه
the investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
On 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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For a compact convex set K ⊂ C the well-known general Markov inequality holds asserting that a polynomial p of degree n must have ∥∥p′∥∥ c(K)n2 ‖p‖. On the other hand for polynomials in general, ∥∥p′∥∥ can be arbitrarily small as compared to ‖p‖. The situation changes when we assume that the polynomials in question have all their zeroes in the convex set K. This was first investigated by Turán,...
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By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.
متن کاملConvex Interpolation by Splines of Arbitrary Degree
An algorithm is described for computing an interpolation spline of arbitrary but fixed degree which preserves the convexity of the given data set. Necessary and sufficient conditions for the solvability of the problem, some special cases and error estimations are given.
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1980
ISSN: 0021-9045
DOI: 10.1016/0021-9045(80)90080-5