Affine Projection Model
Affine arithmetic can be viewed in matrix form as follows. Let be all input and computed quantities in use at some point during a computation. The affine forms for those quantities can be represented by a single coefficient matrix A and a vector b, where element is the coefficient of symbol in the affine form of ; and is the independent term of that form. Then the joint range of the quantities — that is, the range of the point — is the image of the hypercube by the affine map from to defined by .
The range of this affine map is a zonotope bounding the joint range of the quantities . Thus one could say that AA is a "zonotope arithmetic". Each step of AA usually entails adding one more row and one more column to the matrix A.
Read more about this topic: Affine Arithmetic
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