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arXiv 1504.01964math.NAcs.NA
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一种兰伯特型函数的稳健近似

A Robust Approximation to a Lambert-Type Function

Physics and Astronomy Department, Western University(西方大学物理与天文系)

Ken Roberts

AI总结:

本文提出一种稳健算法,用于计算兰伯特型函数 $y = g(x) = \mathrm{log}(W(e^x))$,解决了由于计算精度问题导致的数值不稳定性,适用于大多数可表示的 $x$ 值。

摘要:

函数 $y = g(x) = \mathrm{log}(W(e^x))$ 是方程 $y + e^y = x$ 的解,出现在如太阳能电池板电流-电压曲线计算等场景中。由于直接计算 $g(x)$ 可能因算术下溢或上溢而不准确,本文提出一种简单算法,该算法在不依赖所选计算机语言中实现的兰伯特 W 函数的情况下,能够稳健地计算 $g(x)$,适用于几乎所有可表示的 $x$ 值。

英文摘要:

The function $y = g(x) = \mathrm{log}\big(W(e^x)\big)$, where $W()$ denotes the Lambert W function, is the solution to the equation $y + e^y = x$. It appears in various problem situations, for instance the calculation of current-voltage curves for solar cells. A direct calculation of $g(x)$ may be inaccurate because of arithmetic underflow or overflow. We present a simple algorithm for calculating $g(x)$ that is robust, in that it will work for almost all $x$ values which are representable in the arithmetic of one's chosen computer language. The algorithm does not assume that the chosen computer language implements the Lambert W function.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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