Article citationsMore>>

K. Weierstrass, “Uber die analytische Darstellbarkeit sogenannter willkurlicher Functionen einer reellen Veranderlichen Sitzungsberichteder,” Koniglich Preussischen Akademie der Wissenschcaften zu Berlin, 1885, pp. 633-639 & pp. 789-805.

has been cited by the following article:

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

  AUTHORS: Shanaz Ansari Wahid

  KEYWORDS: Approximation, Bernstein Operator, Dual-Fusion, Simulated Empirical Study

  JOURNAL NAME: Applied Mathematics, Vol.2 No.12, December 27, 2011

  ABSTRACT: 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.