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quadrature rule using Lagrange

Roy Vincent L. Canseco, MSEE     Jan 2014

An interpolating function fits the data points exactly. Quadrature rules are based on polynomial interpolation. The integral of the interpolant approximates the integral of the function of interest.

An n-point quadrature formula is of the form


It is approximated by a quadrature rule of the form    

We integrate a polynomial interpolant to come up with a quadrature rule.

The Lagrange polynomial for datapoints  (t[i], y[i])  is of the form

We integrate that.


Comparing the above with the quadrature rule and taking into account that y[i]  in the data set is equal to  the value of function f at t[i] , we determine that  the  weights function  w(t[i])  for this case must be