Representations of Intervals and Optimal Error Bounds.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Calculations with interval arithmetic and interval extensions of real functions are often used to obtain lower and upper bounds for what would be the theoretical results of precise computations on exact data. A more traditional way to represent approximate data and results contained in intervals is by means of a representative point x in the interval and an associated measure of error E. For example, the midpoint of an interval has absolute error as an approximation to other points of the interval which is bounded by half the width of the interval. In general, the chosen point is said to be optimal with respect to the measure of error if the maximum value of E over the interval is minimized. A general method for determination of optimal points x and minimal error bounds E is given.
- Theoretical Mathematics