One may use the online calculator to perform basic in- terval arithmetic and set operations as well as to bound standard interval functions. ... greatest lower bound and the least upper bound re- .... tation of divided by the input integer param-.
An Online Interval Calculator Ming-chi Hung and Chenyi Hu Department of Computer and Mathematical Sciences University of Houston-Downtown Houston, Texas 77002
Abstract| In this paper, we report the motivation, design, implementation, and usage of an online interval calculator which we developed very recently. The online interval calculator is, in fact, a Java applet [9]. It can be accessed interactively through the world wide web. One may use the online calculator to perform basic interval arithmetic and set operations as well as to bound standard interval functions. I. Introduction and Motivation
A. Introduction Interval arithmetic [1, 10, 11], rst introduced by Moore in the 1960's, has become a useful computing tool in scienti c research and applications. In interval computing, all operations are performed directly on machine representable intervals. Comparing with the commonly used oating point arithmetic, interval computation has the following advantages. 1. Computing results obtained with nite digits
oating point arithmetic may be unreliable. Instead, interval computing provides reliable solution bounds. 2. Interval arithmetic can be directly applied to bound interval terms which frequently appeared in some important computational mathematical theorems. For example, the remainder term in Taylor theorem can be directly bounded with interval computing. 3. Intervals can be used to better model application problems. Input data measured from real world as well as control parameters are usually within certain ranges (intervals) rather than precise points. 4. Interval computing supports more operations than oating point arithmetic. For example, set operations can be performed directly with intervals.
With these advantages, researchers have solved some otherwise very hard to solve problems such as nding reliable global optimum [4] and solving nonlinear systems of equations [6]. In application areas such as in electrical engineering [12], chemical engineering [14], expert systems, economics, and other areas [7], researchers have also made progresses with interval methods. B. The Motivation The facts below motivated us to develop this software package. Signi cant achievements have been made with interval computing, however, many people still do not know it. Most currently available interval software packages do not have interactive graphical user interfaces for basic interval computing. That makes it hard for beginners to learn and to apply interval computing. Interval calculators are not available to general users. To make fundamental interval computing easy to access, and to provide people a convenient interval computing tool, we developed the Internet accessible online interactive interval calculator. II. The Design
A. Objectives The software package of the online interval calculator should meet the following objectives: 1. Reliably performing interval operations; 2. Having a user-friendly interactive graphical user interface; 3. Portable across di erent machine platforms and operating systems; 4. Accessible through the Internet; and 5. Easy to maintain and to update. B. Intervals and Directed Rounding This software package mainly deals with real intervals. Only machine representable intervals, whose This research was partially supported by NSF grants CCR- lower and upper bounds are oating point repre9503757, CDA-9522157; DoD/ARO grant DAAH-0495-1-0250, and Sun Microsystems. sentable, can be stored and processed on oating
point machines. To achieve reliability, it is required interval inverse cosine, that any machine representation of a mathemati interval inverse tangent, cal interval [a; b], which is the set fx 2
