V2EX least-squares

Least-Squares

释义 Definition

最小二乘法:一种数学/统计方法,通过最小化“残差”(观测值与模型预测值之差)的平方和来拟合模型参数(常用于回归、曲线拟合、数据平滑等)。也常指“最小二乘估计/拟合”(least-squares estimation/fitting)。

发音 Pronunciation (IPA)

/list skwrz/

例句 Examples

We used least-squares to fit a line to the data.
我们用最小二乘法把一条直线拟合到这些数据上。

The engineer applied a least-squares approach to estimate the parameters, reducing the impact of random measurement noise across multiple trials.
工程师采用最小二乘方法来估计参数,从而在多次试验中减弱随机测量噪声的影响。

词源 Etymology

“least”表示“最小的”,“squares”指“平方项”。该术语直观描述了方法的核心:在所有可能的拟合方案中,选择让误差的平方和最小的那一个。作为系统化的计算方法,最小二乘法在1819世纪逐渐发展成熟,并在天文学测量与误差处理等领域得到广泛应用。

相关词 Related Words

文学作品 Literary Works

  • Mary L. Boas, Mathematical Methods in the Physical Sciences(常在数据拟合与误差分析章节讲到 least-squares)
  • William H. Press et al., Numerical Recipes(数值计算中回归与拟合部分频繁出现 least-squares)
  • Carl Friedrich Gauss 相关论文与著述(在误差理论与天文测量背景中讨论最小二乘思想与方法)
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