Interval Arithmetic, Affine Arithmetic, Taylor Series Methods: Why, What Next?
نویسندگان
چکیده
منابع مشابه
Modified Affine Arithmetic Is More Accurate than Centered Interval Arithmetic or Affine Arithmetic
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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We study the performance of affine arithmetic as a replacement for interval arithmetic in interval methods for ray casting implicit surfaces. Affine arithmetic is a variant of interval arithmetic designed to handle the dependency problem, and which has improved several interval algorithms in computer graphics.
متن کاملWhy Interval Arithmetic is so Useful
Interval arithmetic was introduced by Ramon Moore [Moo66] in the 1960s as an approach to bound rounding errors in mathematical computation. The theory of interval analysis emerged considering the computation of both the exact solution and the error term as a single entity, i.e. the interval. Though a simple idea, it is a very powerful technique with numerous applications in mathematics, compute...
متن کاملAffine 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...
متن کاملImplementing Taylor models arithmetic with floating-point arithmetic
The implementation of Taylor models arithmetic may use floating-point arithmetic to benefit from the speed of the floatingpoint implementation. The issue is then to take into account the roundoff errors. Here, we assume that the floating-point arithmetic is compliant with the IEEE-754 standard. We show how to get tight bounds of the roundoff errors, and more generally how to get high accuracy f...
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ژورنال
عنوان ژورنال: Numerical Algorithms
سال: 2004
ISSN: 1017-1398
DOI: 10.1023/b:numa.0000049478.42605.cf