"Quick and dirty" Solve[]
in [Mathematica]
|
From: guerom00 on 23 Mar 2010 05:23 Hello all, In order to found an upper bound for a numerical integration, I would like to "solve" something like Solve[f[x]<1*^-10,x] but in a quick and dirty way; let me explain : - dirty, in the sense that I would be happy to find an x for which f[x] is say between 1*^-9 and 1*^-11 or so - quick in the sense that one evaluation of f[x] takes some time; the goal would be to find x by evaluating f[x] as fewer time as possible Any idea how to do that ? Thanks in advance
From: Bill Rowe on 24 Mar 2010 05:32 On 3/23/10 at 4:24 AM, guerom00(a)gmail.com (guerom00) wrote: >In order to found an upper bound for a numerical integration, I >would like to "solve" something like Solve[f[x]<1*^-10,x] but in a >quick and dirty way; let me explain : - dirty, in the sense that I >would be happy to find an x for which f[x] is say between 1*^-9 and >1*^-11 or so - quick in the sense that one evaluation of f[x] takes >some time; the goal would be to find x by evaluating f[x] as fewer >time as possible >Any idea how to do that ? There are several possible ways to approach such a problem. But to make good suggestions, I really need to know something about your f[x]. A couple of possibilities. Plot f[x] over a suitable range. Find a functions h such that f[x]<h[x] over the appropriate range that is easier to evaluate. A useful function h would not be much different than f and would have similar limiting behavior.
From: dh on 24 Mar 2010 05:35 Hi, look e.g. at: FindInstance. Daniel On 23.03.2010 10:23, guerom00 wrote: > Hello all, > > In order to found an upper bound for a numerical integration, I would > like to "solve" something like Solve[f[x]<1*^-10,x] but in a quick and > dirty way; let me explain : > - dirty, in the sense that I would be happy to find an x for which > f[x] is say between 1*^-9 and 1*^-11 or so > - quick in the sense that one evaluation of f[x] takes some time; the > goal would be to find x by evaluating f[x] as fewer time as possible > > Any idea how to do that ? > > Thanks in advance > -- Daniel Huber Metrohm Ltd. Oberdorfstr. 68 CH-9100 Herisau Tel. +41 71 353 8585, Fax +41 71 353 8907 E-Mail:<mailto:dh(a)metrohm.com> Internet:<http://www.metrohm.com>
From: guerom00 on 24 Mar 2010 06:03 FindInstance[] doesn't help... For what it's worse, I know how my function f(x) behaves. It is always negative, increasing and goes to zero when x goes to infinity. A kind of root finding method based on the bisection method e.g. should do the trick...
From: Bill Rowe on 25 Mar 2010 05:26
On 3/24/10 at 5:03 AM, guerom00(a)gmail.com (guerom00) wrote: >FindInstance[] doesn't help... For what it's worse, I know how my >function f(x) behaves. It is always negative, increasing and goes to >zero when x goes to infinity. A kind of root finding method based on >the bisection method e.g. should do the trick... Then you might find Ted Ersek's RootSearch package useful. It can be obtained from Wolfram's web site. |