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Results tagged with rootfinding
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user 10366
Algorithms to approximate numerically a root of a nonlinear equation or system: for instance, Newton's method, secant method, bisection, etc.
6
votes
how to solve $\sum_{i=0}^n (x-\mu_i)e^{-(x-\mu_i)^2} = 0$
It is simple to reduce to the case where $\sum_i\mu_i=0$. Then the simplest nontrivial case is $(x-\mu)e^{-(x-\mu)^2}+(x+\mu)e^{-(x+\mu)^2}=0$, which is equivalent to $(x+\mu)/(x-\mu)=e^{4x\mu}$. He …
- 56.9k
0
votes
Rigorous estimates on roots of function
Put $a_k=1+\sin(k\pi/(2N))^2$, so $f(x)=1-N^{-1}\sum_{k=1}^N(a_k-1)/(a_k-x)$. Let $b_k$ be the unique root of $f(x)$ lying in $[a_{k-1},a_k]$, and put $t_k=(b_k-a_{k-1})/(a_k-a_{k-1})$, so $t_k$ meas …
- 56.9k