Chebfun and numerical quadrature

Chebfun: A New Kind of Numerical Computing

The functionalities of the chebfun and chebop systems are surveyed. The chebfun system is a collection of Matlab codes to manipulate functions in a manner that resambles symbolic computing. The operations, however, are performed numerically using polynomial representations. Chebops are built with the aid of chebfuns to represent linear operators and allow chebfun solutions of differential equat...

Numerical Quadrature: Theory and Computation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Chapter

Numerical Quadrature and Asymptotic Expansions

Numerical Quadrature of Fourier Transform

In some cases the function <£(£) or \pik) is given by a closed expression which is too complicated to permit a sufficiently accurate analytic evaluation of the integral for the entire range of the parameter x. In other cases 4>ik) or ^(&) may be available only in numerical form. The conventional methods of numerical quadrature (e.g., Simpson's rule) are not suitable for evaluation of the above ...

Numerical Quadrature of Fourier Transform

In some cases the function <£(£) or \pik) is given by a closed expression which is too complicated to permit a sufficiently accurate analytic evaluation of the integral for the entire range of the parameter x. In other cases 4>ik) or ^(&) may be available only in numerical form. The conventional methods of numerical quadrature (e.g., Simpson's rule) are not suitable for evaluation of the above ...