Asymptotic approximation by polynomials in the L1 norm
نویسندگان
چکیده
منابع مشابه
Best one-sided approximation of polynomials under L1 norm
In this paper, we develop an analytic solution for the best one-sided approximation of polynomials under L1 norm, that is, we 0nd two polynomials with lower degree which bound the given polynomial such that the areas between the bounding polynomials and the given polynomial attain minimum. The key ingredient of our technique is a characterization for one-sided approximations based on orthogonal...
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In the paper we review some known results about the one-sided approximation of polynomials with lower-degree polynomials under L1 norm. Then based on these results, the approximation error is formulated. Some properties are also stated for the general cases. The approximation can be used in the degree reduction of interval polynomials and interval Bézier curves.
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As usual, p∗ is called a best approximation (b.a.) to f in (or, by elements of) IPγ,n. To give some examples, let X = Lp[0, 1] and set γ(t) = G(·, t), where G(s, t) is defined on [0, 1] × T . With G Green’s function for a k–th order ordinary linear initial value problem on (0, 1] and T = [0, 1), one has approximation by generalized splines. With G(s, t) = e and T = IR, one has approximation by ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1973
ISSN: 0021-9045
DOI: 10.1016/0021-9045(73)90002-6