Interpolation Error
where,
- true function
- approximating polynomial
- interpolation error error
Quadrature Error
or
where,
- exact integral
- quadrature approximation
Some common Quadrature error expansions
Simple Left/Right Rectangle Rules ()
These methods are not symmetric, so their error expansion includes all powers of , starting with an term.
Summed Trapezoidal Rule / Summed Trapezoidal Rule ():
term and proceeds in even powers.
Simpson’s rule ()
The error for starts at order .