Approximand

Approximand is a term used in certain areas of mathematics and numerical analysis to denote the object that is being approximated in an approximation process. In this usage, the approximand is the exact, true, or intended quantity, value, or object that an approximant seeks to resemble or approach.

Usage and scope

The term is not part of standard, widely adopted mathematical vocabulary and appears mainly in specialized or older texts. It is often contrasted with approximant, the result produced by an approximation method. The distinction is used to emphasize the target of the approximation (the approximand) versus the actual computed or constructed result (the approximant). Because the term is relatively uncommon today, many writers prefer more familiar phrasing such as “the exact value,” “the target value,” or “the solution,” rather than “approximand.”

Examples

In numerical solving of equations, the exact root a of an equation is the approximand, while the iterates produced by the method are the approximants. In function approximation, the actual function value f(x) at a given x can be regarded as the approximand, with the approximated value f̂(x) serving as the approximant. In geometric modeling, the true shape or surface may be the approximand, and its simplified representation is the approximant.

See also

- Approximant

- Approximation

- Target value

- Exact solution

Notes

Due to its limited use, readers encountering approximand should consider the surrounding context to confirm whether the term is being used as a formal label or simply as a descriptive phrase for the quantity being approximated.