Abstract: We study the reliability and performance of interval arithmetic for ray tracing implicit surfaces. We analyze when and how to use interval arithmetic as an alternative to the methods used in ...

Abstract: A novel affine arithmetic (AA) method with missed triangular domain (remaining area is convex polygons) is proposed in this paper for solving interval power flow (IPF) problem with ...

We implement conservative interval arithmetic in Lean, on top of a software implementation of floating point (since Lean's Float is untrusted). The key types are ...

This paper introduces a novel extension of interval arithmetic through the formulation of pseudo- complex numbers, a mathematical framework defined over the quotient of polynomials R[h] (h2−h) . By ...

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This paper first exposes some of the defects in the interval arithmetic algorithms of Moore and Krückeberg. Then it identifies classes of problems on which these algorithms compute "optimum bounds".

Floating-point arithmetic is a cornerstone of modern computational science, providing an efficient means to approximate real numbers within a finite precision framework. Its ubiquity across scientific ...