منابع مشابه
Polynomial Approximation
Polynomials are very simple mathematical functions which have the flexibility to represent very general nonlinear relationships. Approximation of more complicated functions by polynomials is a basic building block for many numerical techniques. This article considers two distinct but related applications. The first is polynomial regression in which polynomials are used to model a nonlinear rela...
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Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are coconvex with it, namely, polynomials and piecewise polynomials that change their convexity exactly at the points where f does. We obtain Jackson type estimates and summarize the positive and negative...
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Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hubert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer o...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1974
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1974.51.491