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Interval arithmetic, interval mathematics, interval analysis, or interval computation, is a method developed by mathematicians since the 1950s and 1960s as an approach to putting bounds on rounding errors and measurement errors in mathematical computation and thus developing numerical methods that yield reliable results. Very simply put, it represents each value as a range of possibilities. For example, instead of estimating the height of someone using standard arithmetic as 2.0 metres, using interval arithmetic we might be certain that that person is somewhere between 1.97 and 2.03 metres. This concept is suitable for a variety of purposes. The most common use is to keep track of and handle rounding errors directly during the calculation and of uncertainties in the knowledge of the exact values of physical and technical parameters. The latter often arise from measurement errors and tolerances for components or due to limits on computational accuracy. Interval arithmetic also helps find reliable and guaranteed solutions to equations and optimization problems. Mathematicly, instead of working with an uncertain real we work with the two ends of the interval which contains . In interval arithmatic, any variable lies between and , or could be one of them. A function when applied to is also uncertain. In interval arithmetic produces an interval which is all the possible values for for all . ==Introduction== The main focus in the interval arithmetic is on the simplest way to calculate upper and lower endpoints for the range of values of a function in one or more variables. These barriers are not necessarily the supremum or infimum, since the precise calculation of those values can be difficult or impossible. Treatment is typically limited to real intervals, so quantities of form : where and are allowed; with one of them infinite we would have an unbounded interval, while with both infinite we would have the extended real number line. As with traditional calculations with real numbers, simple arithmetic operations and functions on elementary intervals must first be defined. More complicated functions can be calculated from these basic elements.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「interval arithmetic」の詳細全文を読む スポンサード リンク
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