Affine arithmetic (AA) is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations (affine forms) of certain primitive variables, which stand for sources of uncertainty in the data or approximations made during the computation.
Affine arithmetic is meant to be an improvement on interval arithmetic (IA), and is similar to generalized interval arithmetic, first-order Taylor arithmetic, the center-slope model, and ellipsoid calculus — in the sense that it is an automatic method to derive first-order guaranteed approximations to general formulas.
Affine arithmetic is potentially useful in every numeric problem where one needs guaranteed enclosures to smooth functions, such as solving systems of non-linear equations, analyzing dynamical systems, integrating functions differential equations, etc. Applications include ray tracing, plotting curves, intersecting implicit and parametric surfaces, error analysis, process control, worst-case analysis of electric circuits, and more.
Read more about Affine Arithmetic: Definition, Affine Arithmetic Operations, Affine Projection Model, Affine Form Simplification
Famous quotes containing the word arithmetic:
“I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.”
—Gottlob Frege (1848–1925)