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Best Copositive Approximation

โœ Scribed by J. Zhong

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
616 KB
Volume
72
Category
Article
ISSN
0021-9045

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We prove that if a function \(f \in \mathbb{C}[0,1]\) changes sign finitely many times, then for any \(n\) large enough the degree of copositive approximation to \(f\) by quadratic spliners with \(n-1\) equally spaced knots can be estimated by \(C \omega_{2}(f, 1 / n)\), where \(C\) is an absolute c

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It is known that shape preserving approximation has lower rates than unconstrained approximation. This is especially true for copositive and intertwining approximations. For f # L p , 1 p< , the former only has rate | . ( f, n &1 ) p , and the latter cannot even be bounded by C & f & p . In this pap