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Numerieke Differentiatie Formules
Numerieke Integratie Formules

Closed Newton–Cotes Formulae
Degree Common name Formula Error term
1 Trapezoid rule
2 Simpson's rule
3 Simpson's 3/8 rule
4 Boole's rule
Closed Newton–Cotes Formulae
Degree Common name Formula Error term
1 Trapezoid rule
2 Simpson's rule
3 Simpson's 3/8 rule
4 Boole's rule
Closed Newton–Cotes Formulae
Degree Common name Formula Error term
1 Trapezoid rule
2 Simpson's rule
3 Simpson's 3/8 rule
4 Boole's rule

Constructing the interpolation polynomial

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The red dots denote the data points (xk,yk), while the blue curve shows the interpolation polynomial.

Suppose that the interpolation polynomial is in the form

 

The statement that p interpolates the data points means that

 

If we substitute equation (1) in here, we get a system of linear equations in the coefficients  . The system in matrix-vector form reads

 

We have to solve this system for   to construct the interpolant   The matrix on the left is commonly referred to as a Vandermonde matrix.

 
 

of Lagrange basis polynomials