منابع مشابه
Weak Copositive and Intertwining Approximation
It is known that shape preserving approximation has lower rates than unconstrained approximation. This is especially true for copositive and intertwining approximations. For f 2 L p , 1 p < 1, the former only has rate ! ' (f; n ?1) p , and the latter can not even be bounded by Ckfk p. In this paper, we discuss various ways to relax the restrictions in these approximations and conclude that the ...
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For a function f 2 L p ?1; 1], 0 < p < 1, with nitely many sign changes, we construct a sequence of polynomials P n 2 n which are copositive with f and such that kf ? P n k p C! ' (f; (n + 1) ?1) p , where ! ' (f; t) p denotes the Ditzian-Totik modulus of continuity in L p metric. It was shown by S. P. Zhou that this estimate is exact in the sense that if f has at least one sign change, then ! ...
متن کاملPositive and Copositive Spline Approximation in L P 0; 1]
The order of positive and copositive spline approximation in the L p-norm, 1 p < 1, is studied, the main results are (1) the error of positive approximation by splines is bounded by C! 2 (f; 1=n) p if f has a nonnegative extension; (2) the order deteriorates to ! 1 if f does not have such an extension; (3) the error of copositive spline approximation is bounded by C!(f; 1=n) p ; (4) if f is als...
متن کاملPolynomial 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...
متن کاملAn Adaptive Linear Approximation Algorithm for Copositive Programs
We study linear optimization problems over the cone of copositive matrices. These problems appear in nonconvex quadratic and binary optimization; for instance, the maximum clique problem and other combinatorial problems can be reformulated as such problems. We present new polyhedral inner and outer approximations of the copositive cone which we show to be exact in the limit. In contrast to prev...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1974
ISSN: 0021-9045
DOI: 10.1016/0021-9045(74)90071-9