Numerical Methods Max Point

  • Thread starter brydustin
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I have a function with one and only one local/global maxium.... (i.e. half the function has positive slope, half the function has negative slope). And I want to find the maximum point on the function. How can I find the function's max?

I was thinking of turning the function into its derivative and using Newton's Method for finding the zero..... are there better ways?
 

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  • #2
HallsofIvy
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Yes, that will work. Another way, that will converge slower does not require finding the derivative (and the second derivative to use Newton's method) is this:

Choose two points, p and q, and an interval length, [itex]\delta[/itex]. If f(p)> f(q), choose a new point, r, a distance [itex]\delta[/itex] beyond p (opposite the direction from p to q. If f(q)> f(p), reverse p and q). If f(r)> f(p), repeat. If f(r)< f(p) reverse direction and divide [itex]\delta[/itex] by 2 to halve the interval length.

Since this question has nothing to do with differential equations, I am moving it to "Calculus and Analysis".
 

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