最小二乗法による放物線およびガウス関数の迅速な計算法とその工学への応用

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  • Simplified equations for rapidly calculating a parabola and a Gaussian function by the least-squares method with engineering applications.
  • サイショウ 2ジョウホウ ニ ヨル ホウブツセン オヨビ ガウス カンスウ ノ

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For engineering purposes, it often becomes necessary to fit a parabola and a Gaussian function to equally spaced n data points (xi, yi) by using the least squares method. Simplified equations for calculating these functions are derived for rapid calculation and to avoid error due to the overflow of figures in the calculation with a computer. The coefficients of the parabola given by y=a(x-x^-)2+b(x-x^-)+c are [numerical formula] where, x^- is the mean and e is a fixed interval of x and [numerical formula] For a Gaussian function given by y=exp[a(x-x^-)2+b(x-x^-)+c], the coefficients can be calculated from Eq(1) using ci, and substituting ln yi for yi in Eq(2).

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