Numerical integration constants

Recognizing Numerical Constants

The advent of inexpensive, high-performance computers and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now exist for determining, within certain limits, whether a computed real or complex number can be written as a simple expression involving the classical constants of mathematics. These techniques will be il...

Numerical Estimation of Projection Constants

Numerical integration using spline quasi-interpolants

In this paper, quadratic rules for obtaining approximate solution of definite integrals as well as single and double integrals using spline quasi-interpolants will be illustrated. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.

Numerical Integration

i=0 if(xi): (2) i.e., we express the numerical approximation to the integral I(f) as a sum of a series of nite number of terms, each term containing the value of the function at a given point xi weighted by a coe cient i. One way to determine the coe cients i is to replace the original function f(x) by an interpolating function which is simple enough, or in the terminology of numerical analysts...

Numerical Integration

This article focuses on the process of approximating a definite integral from values of the integrand when exact mathematical integration is not available. This problem arises in statistics when marginal density functions or expected values of random variables are required. The article describes classical univariate quadrature methods including the trapezoidal rule, Simpson’s rule, Newton-Cotes...