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An approximation is anything that is similar but not exactly equal to something else. The term can be applied to various properties (e.g. value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g. the approximate time was 10 o'clock). Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. In science, approximation can refer to using a simpler process or model when the correct model is difficult to use. An approximate model is used to make calculations easier. Approximations might also be used if incomplete information prevents use of exact representations. The type of approximation used depends on the available information, the degree of accuracy required, the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation. == Mathematics == Approximation theory is a branch of mathematics, a quantitative part of functional analysis. Diophantine approximation deals with approximations of real numbers by rational numbers. Approximation usually occurs when an exact form or an exact numerical number is unknown or difficult to obtain. However some known form may exist and may be able to represent the real form so that no significant deviation can be found. It also is used when a number is not rational, such as the number π, which often is shortened to 3.14159, or √2 to 1.414. Numerical approximations sometimes result from using a small number of significant digits. Calculations are likely to involve rounding errors leading to approximation. Log tables, slide rules and calculators produce approximate answers to all but the simplest calculations. The results of computer calculations are normally an approximation expressed in a limited number of significant digits, although they can be programmed to produce more precise results.〔(Numerical Computation Guide )〕 Approximation can occur when a decimal number cannot be expressed in a finite number of binary digits. Related to approximation of functions is the asymptotic value of a function, i.e. the value as one or more of a function's parameters becomes arbitrarily large. For example, the sum (''k''/2)+(''k''/4)+(''k''/8)+...(''k''/2^''n'') is asymptotically equal to ''k''. Unfortunately no consistent notation is used throughout mathematics and some texts will use ≈ to mean approximately equal and ~ to mean asymptotically equal whereas other texts use the symbols the other way around. As another example, in order to accelerate the convergence rate of evolutionary algorithms, fitness approximation—that leads to build model of the fitness function to choose smart search steps—is a good solution. 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「Approximation」の詳細全文を読む スポンサード リンク
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