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:
“Truth is the kind of error without which a certain species of life could not live. The value for life is ultimately decisive.”
—Friedrich Nietzsche (18441900)
“A higher class, in the estimation and love of this city- building, market-going race of mankind, are the poets, who, from the intellectual kingdom, feed the thought and imagination with ideas and pictures which raise men out of the world of corn and money, and console them for the short-comings of the day, and the meanness of labor and traffic.”
—Ralph Waldo Emerson (18031882)