An Efficient Combinatorial-Probabilistic Dual-Fusion Modification of Bernstein’s Polynomial Approximation Operator

• 作者: Shanaz Ansari Wahid
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: APPROXIMATION BERNSTEIN Operator Dual-Fusion Simulated Empirical Study
• 年，卷（期）: 2011,（12）
• 页码范围: 1535-1538
• 页数: 4页
• 分类号: O1

摘要

The celebrated Weierstrass Approximation Theorem (1885) heralded intermittent interest in polynomial approximation, which continues unabated even as of today. The great Russian mathematician Bernstein, in 1912, not only provided an interesting proof of the Weierstrass’ theorem, but also displayed a sequence of the polynomials which approximate the given function . An efficient ‘Combinatorial-Probabilistic Dual-Fusion’ version of the modification of Bernstein’s Polynomial Operator is proposed. The potential of the aforesaid improvement is tried to be brought forth and illustrated through an empirical study, for which the function is assumed to be known in the sense of simulation.