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Polynomial Approximation and . . .
, 2007
"... About twenty years ago the measure of smoothness ω r ϕ(f,t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time. ..."
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About twenty years ago the measure of smoothness ω r ϕ(f,t) was introduced and related to the rate of polynomial approximation. In this article we survey developments about this and related concepts since that time.
Polynomial Approximation
, 1997
"... function, and especially on how small the maximum error can be made. Very high order polynomials may be used here if they provide accurate approximations. Very often a function is not approximated directly, but is first transformed or standardized so to make it more amenable to polynomial approximat ..."
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function, and especially on how small the maximum error can be made. Very high order polynomials may be used here if they provide accurate approximations. Very often a function is not approximated directly, but is first transformed or standardized so to make it more amenable to polynomial
SEGMENTATION OF IMAGES USING GRADIENT METHODS AND POLYNOMIAL APPROXIMATION
"... polynomial approximation ..."
Iterated Bernstein polynomial approximations
, 909
"... Iterated Bernstein polynomial approximations of degree n for continuous function which also use the values of the function at i/n, i = 0,1,...,n, are proposed. The rate of convergence of the classic Bernstein polynomial approximations is significantly improved by the iterated Bernstein polynomial ap ..."
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Iterated Bernstein polynomial approximations of degree n for continuous function which also use the values of the function at i/n, i = 0,1,...,n, are proposed. The rate of convergence of the classic Bernstein polynomial approximations is significantly improved by the iterated Bernstein polynomial
More on Comonotone Polynomial Approximation
 in Lp [\Gamma1; 1], 0 ! p 1, Acta Math. Hungarica 77
"... . The main achievement of this article is that we show what was to us a surprising conclusion, namely, twice continuously differentiable functions in (0,1) (with some regular behavior at the endpoints) which change monotonicity at least once in the interval are approximable better by comonotone poly ..."
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polynomials, than such functions which are merely monotone. We obtain Jackson type estimates for the comonotone polynomial approximation of such functions which are impossible to achieve for monotone approximation. 1. Introduction and main results Denote by Y s , s 1, the collection of all sets Y := Y s : 0
Weighted Polynomial Approximation on the Integers By
"... We prove here some polynomial approximation theorems, somewhat related to the SzaszMfintz theorem, but where the domain of approximation is the integers, by dualizing a gap theorem of C. l~Y I for periodic entire functions. In another Paper [7], we shall prove, by similar means, a completeness theo ..."
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We prove here some polynomial approximation theorems, somewhat related to the SzaszMfintz theorem, but where the domain of approximation is the integers, by dualizing a gap theorem of C. l~Y I for periodic entire functions. In another Paper [7], we shall prove, by similar means, a completeness
Polynomial Approximation in SmirnovOrlicz Classes
"... Abstract. We prove a direct theorem for polynomial approximation of functions in certain subclasses of SmirnovOrlicz classes. ..."
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Abstract. We prove a direct theorem for polynomial approximation of functions in certain subclasses of SmirnovOrlicz classes.
The Degree of Coconvex Polynomial Approximation
"... . Let f 2 C[\Gamma1; 1] change its convexity finitely many times in the interval, say s times, at Ys : \Gamma1 ! y 1 ! \Delta \Delta \Delta ! ys ! 1. We estimate the degree of approximation of f by polynomials of degree n, which change convexity exactly at the points Ys . We show that provided n i ..."
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. Let f 2 C[\Gamma1; 1] change its convexity finitely many times in the interval, say s times, at Ys : \Gamma1 ! y 1 ! \Delta \Delta \Delta ! ys ! 1. We estimate the degree of approximation of f by polynomials of degree n, which change convexity exactly at the points Ys . We show that provided n
Computing machineefficient polynomial approximations
 TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2006
"... Polynomial approximations are almost always used when implementing functions on a computing system. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits. And yet ..."
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Cited by 30 (9 self)
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Polynomial approximations are almost always used when implementing functions on a computing system. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits
On the Bernstein Constants of Polynomial Approximation
"... Let α> 0 not be an integer. In papers published in 1913 and 1938, S. N. Bernstein established the limit Λ ∗ ∞,α = lim n→ ∞ nα En [x  α; L ∞ [−1, 1]]. Here En [x  α; L ∞ [−1, 1]] denotes the error in best uniform approximation of x  α on [−1, 1] by polynomials of degree ≤ n. Bernstein prove ..."
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Let α> 0 not be an integer. In papers published in 1913 and 1938, S. N. Bernstein established the limit Λ ∗ ∞,α = lim n→ ∞ nα En [x  α; L ∞ [−1, 1]]. Here En [x  α; L ∞ [−1, 1]] denotes the error in best uniform approximation of x  α on [−1, 1] by polynomials of degree ≤ n. Bernstein
Results 1  10
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9,991