In numerical analysis, Romberg's method (Romberg 1955) is used to estimate the definite integral
by applying Richardson extrapolation (Richardson 1911) 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.
Read more about Romberg's Method: Method, A Geometric Example, Example, Implementation
Famous quotes containing the word method:
“No method nor discipline can supersede the necessity of being forever on the alert. What is a course of history or philosophy, or poetry, no matter how well selected, or the best society, or the most admirable routine of life, compared with the discipline of looking always at what is to be seen? Will you be a reader, a student merely, or a seer? Read your fate, see what is before you, and walk on into futurity.”
—Henry David Thoreau (1817–1862)