Interval Term Rewriting System: Toward A Formal Model for Interval Computation

Interval Term Rewriting System: Toward A Formal Model for Interval Computation

We present a term rewriting system for interval arithmetic (addition, subtraction and multiplication), toward a mathematical model for interval computation. We start presenting a term rewriting system whose rules (directed equations) perform binary floating-point arithmetic, which is based on IEEE-754 Standard. Next, this primitive system is extended with rules for interval arithmetic. Finally,...

Foundations of Interval Computation

This paper reports a study of numerical computation problems from a theoretical viewpoint. It shows that computer systems are not capable of computing of real numbers correctly due to the differences between the algebraic structures of real numbers and model numbers. These two classes of numbers are not isomorphic. From this study, we have learned that there are no machine errors or computation...

Computation of Standard Interval Functions in Multiple-Precision Interval Arithmetic

We present quadratic convergent algorithms for the computation of standard interval functions like √ , ln, arctan in a multiple-precision interval arithmetic. These algorithms depend on elliptic integrals of the first and second kind and the method of arithmetic and geometric means. Представлены квадратично сходящиеся алгоритмы для вычисления стан-дартных интервальных функций, таких как √ , ln,...

A confidence-aware interval-based trust model

It is a common and useful task in a web of trust to evaluate the trust value between two nodes using intermediate nodes. This technique is widely used when the source node has no experience of direct interaction with the target node, or the direct trust is not reliable enough by itself. If trust is used to support decision-making, it is important to have not only an accurate estimate of trust, ...

Interval Computation of Viswanath's Constant