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 .