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Weak Copositive and Intertwining Approximation

✍ Scribed by Y.K. Hu; K.A. Kopotun; X.M. Yu

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
254 KB
Volume
96
Category
Article
ISSN
0021-9045

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✦ Synopsis

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 paper, we discuss various ways to relax the restrictions in these approximations and conclude that the most sensible way is the so-called almost copositiveΓ‚intertwining approximation in which one relaxes the restriction on the approximants in a neighborhood of radius 2 n ( y j ) of each sign change y j .

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