Weights and abscissae of Newton-Cotes quadrature
This functionality does not run in MATLAB.
numeric::ncdata(n) returns the weights and the abscissae of the Newton-Cotes quadrature rule with n equidistant nodes.
The Newton-Cotes quadrature rule produces the exact integral for all polynomials f through degree n - 1. If n is odd, then the quadrature rule is exact through degree n.
The equidistant abscissae c = [c1, …, cn] are given by .
numeric::ncdata is not sensitive to the environment variable DIGITS.
The function uses option remember.
The following call produces exact data for the quadrature rule with four nodes:
List [b,c] is returned. The lists b = [b1, …, bn] and c = [c1, …, cn] are the rational weights and abscissae of the Newton-Cotes quadrature rule, respectively.
The numerical integrator numeric::quadrature calls numeric::ncdata to provide the data for Newton-Cotes quadrature.