Some numerical integration methods based on Bernstein polynomials

Abstract

In this work we find numerical integration of a function by some approximations of the function using Bernstein polynomials, and we introduce a new fast method to approximate the value of a definite integral and we compare them.

Keywords:

• Bernstein polynomial
• Bernoulli polynomials
• numerical integration
• spectral radius

2000 AMS Subject Classifications :

• Primary: 65D30
• 41A10
• Secondary: 65G50
• 65D99

Acknowledgements

The author would be very grateful to the anonymous referees and Prof. Choi-Hong Lai, Editor-in-Chief, for their very nice comments which have been very helpful and valuable in improving this paper.