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The root-finding problem is not solvable in general. In exact real arithmetic, there cannot exist an algorithm that will find an $x$ such that $f(x) = 0$ even i
by ogogmad 6y ago
The root-finding problem is not solvable in general. In exact real arithmetic, there cannot exist an algorithm that will find an $x$ such that $f(x) = 0$ even if such an $x$ exists and $f$ is computable. At least not unless you make some further assumptions about $f$ and $x$.
Of course, I'm talking about the worst case. Your example is easier.
- mehrdadn 6y ago> The root-finding problem is not solvable in general. Great, because nobody was asking for that either. > Of course, I'm talking about the worst case. Your example is easier. Which has been my entire point this whole time, which I already explained to you but which you conveniently prefer to totally ignore. The case I gave is not merely "easier"... it's utterly trivial. I literally even explained how they could solve it with the current algorithm too: by running multiple iterations of that exact algorithm to at least try to get some kind of convergence. Did I ever demand or expect it to solve arbitrary transcendentals? No, nobody was demanding it to magically solve everything. But producing flatly wrong outputs for even the simplest quadratics without any attempt to improve it, sanity check it, or issue a warning is just plain inexcusable and embarrassing.
- deleted 6y ago[deleted]