Romberg Integration Algorithm
A Romberg Integration Algorithm is a definite integral approximation task that ...
- AKA: Romberg's Method.
- See: Werner Romberg, Integration Estimation Algorithm, Integral, Richardson Extrapolation, Trapezium Rule, Rectangle Rule, Newton–Cotes Formulas, Gaussian Quadrature, Clenshaw–Curtis Quadrature.
References
2017
- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Romberg's_method Retrieved:2017-9-16.
- In numerical analysis, Romberg's method is used to estimate the definite integral : [math]\displaystyle{ \int_a^b f(x) \, dx }[/math] by applying Richardson extrapolation repeatedly on the trapezium rule or the rectangle rule (midpoint rule). The estimates generate a triangular array. Romberg's method is a 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 (1909–2003), who published the method in 1955.
- In numerical analysis, Romberg's method is used to estimate the definite integral : [math]\displaystyle{ \int_a^b f(x) \, dx }[/math] by applying Richardson extrapolation repeatedly on the trapezium rule or the rectangle rule (midpoint rule). The estimates generate a triangular array. Romberg's method is a Newton–Cotes formula – it evaluates the integrand at equally spaced points.