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Positivity of cubic polynomials on intervals and positive spline interpolation

✍ Scribed by Jochen W. Schmidt; Walter Heß

Publisher
Springer Netherlands
Year
1988
Tongue
English
Weight
463 KB
Volume
28
Category
Article
ISSN
0006-3835

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On Positive and Copositive Polynomial and Spline Approximation inLp[−1, 1], 0<p<∞
✍ Y.K. Hu; K.A. Kopotun; X.M. Yu 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 610 KB

For a function f # L p [&1, 1], 0< p< , with finitely many sign changes, we construct a sequence of polynomials P n # 6 n which are copositive with f and such that & f &P n & 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