Talk:Bisection method: Difference between revisions

Revision as of 00:42, 11 September 2012

Revision as of 01:50, 12 September 2012

Line 139:

After 15 iterations, it becomes apparent that there is a convergence to about 1.521: a root for the polynomial. [[User:Whlitt|Whlitt]] ([[User talk:Whlitt|talk]]) 00:42, 11 September 2012 (UTC)

== The disadvantage of bisection method ==

I think the bisection method mentioned above can be only used for finding only one root case and it is not effective for multiple roots case. If I assume that the function has multiple roots on [''a'', ''b''] and ''f''(''a'') and ''f''(''b'') have opposite signs,then by using the method above, I can find the midpoint c between a and b. If ''f''(''c'') and ''f''(''b'') have opposite sign, then I can use the new interval [''c'', ''b''] and keep going to find a smaller interval until I find one root on that interval,but in this way, I neglect the possible roots on [''a'', ''c''].Since ''f''(''a'') and ''f''(''c'') have the same sign,I can not apply bisection method to find roots on [''a'', ''c'']. It seems to be difficult to find all the roots of the function on the interval using bisection method because it is hard to know each interval which includes only one root of the function.

So my opinion is to find one of the roots on the interval first by bisection method and then we can apply other methods ,for example Newton's method to find other roots of the function.

[[User:YangOu|YangOu]] ([[User talk:YangOu|talk]]) 01:50, 12 September 2012 (UTC)