A new criterion for best quadrature method

Abstract

In this paper, we introduce an efficient quadrature method adapted to a large class of functions. The idea is to replace the polynomial approximation by a function in Chebyshev space. We describe an algorithm to select the best quadrature method for a given class of functions. This method is determined by solving a minimization of the approximation error. Numerical results are given to show the efficiency of our method.

Subject Classification: [2010]:

• Primary 41A55
• Secondary 41A50

Keywords:

• Quadrature
• Trigonometric bases
• Chebyshev systems
• Numerical integrals