Why is it that a "trial and error" method, choose a value of $x$ and use the right hand side of the equation to find a new value of $x$ and use that new vale of $x$ in the right hand side of the equation etc . . . . . . , to solve for $x$ does not work for an equation of the form $x = -a +b\,e^{-x/c}$, where $a,b$ and $c$ are constants, and yet when rearranged as $x = c\,\ln\left( \dfrac{b} {x+a}\right)$ convergence is very rapid?
Asked
Active
Viewed 61 times
0
-
Usually we cannot predict the sign. So in some cases, we will need more than $\ 2\ $ trials to find a suitable interval having to contain a real root. – Peter Mar 12 '20 at 12:53
-
Basically, the last line summarizes what I have doing all my life (OK : 62+ years of work). – Claude Leibovici Mar 12 '20 at 15:24