Comparison of the Method of Averages with the Method of Least Squares
Comparison of the Method of Averages with the Method of Least Squares
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平均法与最小二乘法的比较
DOI：
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发表时间：
1968
期刊：
影响因子：
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通讯作者：
P. Svensson
中科院分区：
文献类型：
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作者：
G. Dahlquist;B. Sjöberg;P. Svensson
结果表明，对于超定的线性方程组，只要以适当的方式进行分组，计算简单的平均法就能得到令人惊讶的好解。应用线性子空间夹角的概念，对该方法与最小二乘法进行了一般性比较。并以拟合六次以下多项式的检验问题为例说明了该方法的最优应用。
It is shown that the computationally simple method of averages can yield a surprisingly good solution of an overdetermined system of linear equations, provided that the grouping of the equations is done in an appropriate way. The notion of angle between linear subspaces is applied in a general comparison of this method and the method of least squares. The optimal application of the method is treated for the test problem of fitting a polynomial of degree less than six.