Lines of Best Fit for the Zeros and for the Critical Points of a Polynomial
نویسنده
چکیده
Combining results presented in two papers in this Monthly yields the following elementary result. Any line of best fit for the zeros of a polynomial is a line of best fit for its critical points. This note gives a generalization of results on cubic polynomials presented in [1]. Our notation will follow that paper. A line of best fit for a set of points in the plane is defined, as in [1, p. 682], to be a line that minimizes the sum of squares of the perpendicular distances from the points to the line. (Sometimes, elsewhere, such a line is called a “least-squares perpendicular-offsets” line.) Let {zj |1 ≤ j ≤ n} be a set of n ≥ 2 complex numbers. Define zA = 1 n n ∑
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 118 شماره
صفحات -
تاریخ انتشار 2011