# Golden Section Search--When to use it?

• 10-08-2004
just2peachy
Golden Section Search--When to use it?
I have some x inside an interval say [a,b] where I know that my solution lies. Due to the nonlinearity of the problem solving it by traditional agorithms is not possible. I can evaluate each point inside the interval.

I wish to do a search applying the compostion of a few functions to points within the interval until I reached some value close enough to some Epsilon (haven't decided how close I need to be).

I've explored bisecting the interval until I reach the solution, but I was wondering if the Golden section search would be a better choice. Does this converge any faster or am I wasting my time exploring this method? Suggestions anyone?
Thanks,
just2peachy
• 10-08-2004
Sang-drax
If the function is derivable you should try newton-raphson's method.
• 10-08-2004
just2peachy
This function is a composition of function that contains an absolute value, so not sure if derivative will exist.

I'm wondering if the Golden section search is only for unimodal data. If so then would the bisection search be faster in this case since I'm searching for a specific value along a strictly increasing or decreasing interval?
• 10-08-2004
zzzaaahhh
The numerical recipes in C book (http://www.nr.com) contains an extensive chapter on finding roots (chapter 9), with code for a variety of methods, as well as recommendations for shapes of curves where the different methods are likely to work better or worse. Have a look there.
• 10-08-2004
Dave Evans
Quote:

Originally Posted by just2peachy
I have some x inside an interval say [a,b] where I know that my solution lies. Due to the nonlinearity of the problem solving it by traditional agorithms is not possible. I can evaluate each point inside the interval.

I wish to do a search applying the compostion of a few functions to points within the interval until I reached some value close enough to some Epsilon (haven't decided how close I need to be).

I've explored bisecting the interval until I reach the solution, but I was wondering if the Golden section search would be a better choice. Does this converge any faster or am I wasting my time exploring this method? Suggestions anyone?
Thanks,
just2peachy