3

How would I go about solving this sum for $x$?

$$\sum_i\frac{a_i}{(x+b_i)^2}=C$$

Where $\mathbf{a}$ and $\mathbf{b}$ are vectors and $C$ is a constant, and $x$ is a single number. It's for an optimisation routine so if there is no solution getting as close as possible is fine.

Timmmm
  • 244
  • 2
    If you multiply numerator & denominator by $(x+b_j)^2$ for all $j\neq i$ and cross multiply, you'll get a polynomial of $2n$-th degree, where $n$ is the size of $\mathbf{a}$ and $\mathbf{b}$. Then this may be solved using Newton's method or something similar. However, there's probably a better way. – apnorton Jan 02 '15 at 15:36

0 Answers0