Error Estimation
Some quadrature algorithms generate a sequence of results which should approach the correct value. Otherwise one can use a "null rule" which has the form of the above quadrature rule, but whose value would be zero for a simple integrand (for example, if the integrand were a polynomial of the appropriate degree).
See:
- Richardson extrapolation (see also Romberg's method)
- Null rules
- Epsilon algorithm
Read more about this topic: Adaptive Quadrature
Famous quotes containing the words error and/or estimation:
“Error is a supposition that pleasure and pain, that intelligence, substance, life, are existent in matter. Error is neither Mind nor one of Mind’s faculties. Error is the contradiction of Truth. Error is a belief without understanding. Error is unreal because untrue. It is that which seemeth to be and is not. If error were true, its truth would be error, and we should have a self-evident absurdity—namely, erroneous truth. Thus we should continue to lose the standard of Truth.”
—Mary Baker Eddy (1821–1910)
“... it would be impossible for women to stand in higher estimation than they do here. The deference that is paid to them at all times and in all places has often occasioned me as much surprise as pleasure.”
—Frances Wright (1795–1852)