Editing Romberg's method (section)

{{Short description|Numerical integration method}}
{{About|the numerical integration method|the neurological examination maneuver|Romberg's test}}

In [[numerical analysis]], '''Romberg's method'''<ref>{{Harvnb|Romberg|1955}}</ref> is used to estimate the [[Integral|definite integral]] <math display="block"> \int_a^b f(x) \, dx </math> by applying [[Richardson extrapolation]]<ref>{{Harvnb|Richardson|1911}}</ref> repeatedly on the [[trapezium rule]] or the [[rectangle rule]] (midpoint rule). The estimates generate a [[triangular array]].  Romberg's method is a [[Newton–Cotes formulas|Newton–Cotes formula]] – it evaluates the integrand at equally spaced points.
The integrand must have continuous derivatives, though fairly good results
may be obtained if only a few derivatives exist.
If it is possible to evaluate the integrand at unequally spaced points, then other methods such as [[Gaussian quadrature]] and [[Clenshaw–Curtis quadrature]] are generally more accurate.

The method is named after [[Werner Romberg]], who published the method in 1955.