Richardsonkonstanten

Richardsonkonstanten is a term used in the context of Richardson extrapolation, a technique for improving the accuracy of numerical approximations. Specifically, it refers to the constant factor that appears in the leading error term of a numerical method when Richardson extrapolation is applied. The Richardson extrapolation method works by combining results from a numerical method with different step sizes to cancel out the leading error term, thereby increasing the order of accuracy. The Richardsonkonstanten quantifies the coefficient of the error term that remains after this cancellation. Understanding this constant is crucial for analyzing the convergence rate and error behavior of numerical algorithms that employ Richardson extrapolation. It is often derived through Taylor series expansions of the numerical approximation. The specific value of the Richardsonkonstanten depends on the particular numerical method being extrapolated and the function being approximated. In many cases, it is a known analytical quantity, allowing for precise error estimation.