Re: NestWhile and FindRoot[Integrate]
- To: mathgroup at smc.vnet.net
- Subject: [mg42411] Re: [mg42398] NestWhile and FindRoot[Integrate]
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Sat, 5 Jul 2003 03:10:57 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Friday, July 4, 2003, at 01:33 AM, Mukhtar Bekkali wrote:
> I have two questions:
>
> I have function f(x,t), where 0<x<1 and trying to find the value of x
> which
> sets Integrate[f(x,t)g(t),{t,0,1}]=0 for some p.d.f. g(t). So, I
> programmed
> FindRoot[Integrate[f(x,t)g(t),{t,0,1}]==0,{x,0.5}], however, this
> head-on
> approach works only for simple functions f(x,t) and g(t). It seems
> that
> Mathematica is trying to integrate first symbolically and then solve
> it. Is
> there other way to attach the problem?
Since you're using FindRoot, why not use NIntegrate?
>
> Another question relates to loops (totally unrelated to the above
> problem).
> I am trying to find a maximum of function q(y) using Newton's method
> (I want
> to do it manually for my own reasons and do not want to use any
> built-in
> functions). Newton's method essentially substitutes different values
> of y
> into q(y), but in its special way, and then checks if this is the
> maximum.
> So my code is as follows (for some specific functions q(y) and
> parameter z):
>
> y0=0;
> m=D[q(y),y]/D[q(y),{y,2}]
> y1=y0-m/.y->y0;
> NestWhile[{y0=y1,y1=y0-m/.y->y0},{y0,y1},Abs[(q(y)/.y->y1)-(q(y)/.y-
> >y0)]>z]
>
> However, instead of updating y0 and y1 with the old values of y0 and y1
> (i.e. set y0new=y1old and y1new=y0new-m/.y->y0new) it returns the
> initial
> values of y0 and y1 and that's it.
>
You're doing a few things wrong. First, you need q[y], not q(y). Next,
your stopping criterion needs to use q'[y], not q[y]. Finally, the
first and last arguments to NestWhile have to be functions. Try this:
q[y_]:=Sin[y];
y0 = 1.;
z = 10^(-6);
m = q'[y]/q''[y];
y1 = y0 - m /. y -> y0;
step[{y0_, y1_}] := {y1, y1 - m /. y -> y1};
stop[{y0_, y1_}] := With[{dq=q'[y]}, Abs[(dq/.y->y1)-(dq/.y->y0)] > z];
NestWhile[step, {y0, y1}, stop]
-----
Selwyn Hollis
Applied Symbols
http://www.appliedsymbols.com