Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Given an exponentially decaying function $f(x) = e^{-kx}$ that

  • passes through the points $\vec a_0= (x_0, y_0)$ and $\vec a_2 = (x_2, y_2)$
  • such that $x_0 < x_2$ and $y_0 > y_2$,

what is the point $\vec a_1 = (x_1, y_1)$ (where $x_0 < x_1 < x_2$) such that the piecewise linear function passing through points $a$ line segments $\vec a_0 \rightarrow \vec a_1 \rightarrow \vec a_2$ are as close to the curve as possible, that is, that minimizes the integral of the absolute vertical difference between the line segments and $f(x)$?

(At first, I assumed that the $\vec a_1$ would be on the curve, but I don't think it is…)

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.