Mittekompenseerivatena

Mittekompenseerivatena is a term used in numerical analysis to describe a compensated form of the central derivative. It denotes a derivative approximation obtained by augmenting the standard central difference with a compensation term intended to reduce truncation error near a chosen point.

For a sufficiently smooth function f, the standard central difference approximation for f′(x) with step h is Dc(f; x, h) = [f(x + h) − f(x − h)] / (2h). The mittekompenseerivatena M(f; x, h) adds a compensation term E(f; x, h) designed to cancel the leading error term in the Taylor expansion, yielding an improved approximation M ≈ f′(x) + O(h^4) as h → 0. In practice, E is often estimated from the function values at multiple points or by extrapolation, providing a higher-order derivative estimate without requiring explicit higher derivatives.

Usage and reception: The term is not part of standard textbooks and appears only in a limited set of discussions or articles on numerical differentiation. It is described as a conceptual variant of compensated differentiation or as an example of error-balancing techniques rather than a universally adopted method.

Name and etymology: The exact origin of the term is not well documented; it is generally viewed as a coined designation in niche literature, with “mitte” signaling a midpoint notion and “kompenseerivatena” indicating a compensatory derivative, though there is no formal, governing etymology.

See also: central difference, numerical differentiation, error compensation, Richardson extrapolation.