Interval Arithmetic with Some Applications for Digital Computers

摘要

The purpose of this paper is to present a proposed solution to the problem of finding rigorous error bounds, by the use of interval arithmetic. Interval arithmetic is a method of computation in which the rational operations on real numbers are replaced by corresponding operations on closed intervals. That such a replacement is always possible is shown. A discussion is given of interval arithmetic as a system - definitions, operations, theorems, and elementary consequences. An algorithm is presented for the computation of certain functions by the Taylor series, and which has error bounds built into the algorithm. Finally, closed intervals are employed to solve the initial-value first-order differential equation dy dx = f(x,y).