On Affine Arithmetic
نویسندگان
چکیده
منابع مشابه
Affine Arithmetic
We give a formalization of affine forms [1, 2] as abstract representations of zonotopes. We provide affine operations as well as overapproximations of some non-affine operations like multiplication and division. Expressions involving those operations can automatically be turned into (executable) functions approximating the original expression in affine arithmetic. Moreover we give a verified im...
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In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a box-shaped region: (i) using interval arithmetic in centered form is always more accurate than standard affine arithmetic, and (ii) modified affine arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified affine arithmetic is not onl...
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Affine arithmetic (AA) is a model for self-validated computation which, like standard interval arithmetic (IA), produces guaranteed enclosures for computed quantities, taking into account any uncertainties in the input data as well as all internal truncation and roundoff errors. Unlike standard IA, the quantity representations used by AA are first-order approximations, whose error is generally ...
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ABSTRACT. Let G be a compact connected metric abelian group equipped with its normalised Haar measure. Let Tx = a+A(x) be a continuous surjective affine map of G such that γ ≡ 1 is the only character of G satisfying γ ◦A = γ for some positive integer n. Then if φ is a polynomial with real coefficients mapping the natural numbers to themselves, (pl) ∞ l=1 is the sequence of rational primes and f...
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During the development of floating-point signal processing systems, an efficient error analysis method is needed to guarantee the output quality. We present a novel approach to floating-point error bound analysis based on affine arithmetic. The proposed method not only provides a tighter bound than the conventional approach, but also is applicable to any arithmetic operation. The error estimati...
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ژورنال
عنوان ژورنال: Journal of Japan Society for Fuzzy Theory and Intelligent Informatics
سال: 2003
ISSN: 1347-7986,1881-7203
DOI: 10.3156/jsoft.15.155