JOURNAL ARTICLE
高维单形上Bernstein多项式的凸性定理的逆定理
Year: 1989 Journal: Science in China Series A-Mathematics Physics Astronomy & Technological Science (in Chinese) Vol: 19 (6)Pages: 588-599 Publisher: Science China Press
Abstract
设f是m维单形D上的连续函数,Bn(f;x)是f的n次Bernstein多项式. 本文证明:对于D的内点Q,如果恒有Bn(f,Q)≥Bn+1(f,Q),则Q不可能是f的非平凡极大值点. 由此推出,若f在D上是逐块线性函数,则Bn(f,x)≥Bn+1(f,x)(对一切正整数n和任一x∈D)蕴含f是D上的凸函数.
Keywords:
Physics
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Topics
Approximation Theory and Sequence Spaces
Physical Sciences → Mathematics → Statistics and Probability
Advanced Topics in Algebra
Physical Sciences → Mathematics → Algebra and Number Theory
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