closed-form 是什么意思

chibijia

在看论文时经常看到closed-form formula,closed-form solution.请问这里closed-form 做什么意思讲！是闭型讲吗？还是解析之意讲！

sspa

close-form通常指解析表达式； 抄一段wikipedia的解释：

In mathematics, an expression is said to be a closed-form expression if, and only if, it can be expressed analytically in terms of a bounded number of certain "well-known" functions. Typically, these well-known functions are defined to be elementary functions; so infinite series, limits, and continued fractions are not permitted.

Similarly, an equation or system of equations is said to have a closed-form solution if, and only if, at least one solution can be expressed as a closed-form expression.

For example, the roots of any quadratic equation with complex coefficients can be expressed in closed form in terms of addition, subtraction, multiplication, division, and square root extraction, all elementary functions. However, there are quintic equations without closed-form solutions using elementary functions; see Galois theory.

Changing the definition of "well-known" to include additional functions can change the set of equations with closed-form solutions. Many cumulative distribution functions cannot be expressed in closed form, unless one considers special functions such as the error function or gamma function to be well-known. It is possible to solve the quintic equation if general hypergeometric functions are included, although the solution is far too complicated algebraically to be useful. For many practical computer applications, it is entirely reasonable to assume that the gamma function and other special functions are well-known, since numerical implementations are widely available.

妓女的尊严

什么玩意儿

huatian008

什么玩意儿

chibijia

哦，学习了！多谢二楼解释！！！

usb_geek

close form formula通俗的话讲，就是通用的公式。

一类问题的解决如果有了close form formula，就表示有标准的解法（尽管不一定是最佳方案），不管这个问题多么复杂，按照这个close form，就一定能够接出来，所以称为close form. 我的理解是这类问题已经close了。