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Thread Subject:
roots of an asymptotic function

Subject: roots of an asymptotic function

From: Baha Kuzu

Date: 10 Nov, 2010 06:04:03

Message: 1 of 5

For an asymptotic function;

d=sum(n=1 to 20) [ (sin(n))^2 / ( 0.5(-w^2+(n*pi)^4) ) ]=0

I got the plot of function as (d versus w). I used for loop for that plot. There are asymptotes close to every w=(npi)^2 point. I can see these points in plot, and also see the intersection points of the function d on 'w' axis. For example for first intersection(solution) w1=~27.478, and 2nd and 3rd w2=88.15, w3=130.05
But I would like to find these values numerically instead of reading it from plot. Because there is not only 3 w's. There are number of w's. I can't read them from plot. The question briefly is that what are the roots (w's) that makes 'd' function equal to zero.

Any information about that is appreciated.
Thank you...
Baha

Subject: roots of an asymptotic function

From: Alan Weiss

Date: 10 Nov, 2010 13:26:19

Message: 2 of 5

On 11/10/2010 1:04 AM, Baha Kuzu wrote:
> For an asymptotic function;
>
> d=sum(n=1 to 20) [ (sin(n))^2 / ( 0.5(-w^2+(n*pi)^4) ) ]=0
>
> I got the plot of function as (d versus w). I used for loop for that
> plot. There are asymptotes close to every w=(npi)^2 point. I can see
> these points in plot, and also see the intersection points of the
> function d on 'w' axis. For example for first intersection(solution)
> w1=~27.478, and 2nd and 3rd w2=88.15, w3=130.05
> But I would like to find these values numerically instead of reading it
> from plot. Because there is not only 3 w's. There are number of w's. I
> can't read them from plot. The question briefly is that what are the
> roots (w's) that makes 'd' function equal to zero.
>
> Any information about that is appreciated.
> Thank you... Baha

doc fzero

Alan Weiss
MATLAB mathematical toolbox documentation

Subject: roots of an asymptotic function

From: Baha Kuzu

Date: 10 Nov, 2010 14:20:05

Message: 3 of 5

Thank you Alan,

But "fzero" is for the root if you know a close number to it, right? If so, how can I find let's say 30 roots or 50 roots? Can I still use fzero?


Alan Weiss <aweiss@mathworks.com> wrote in message <ibe6hr$ile$2@fred.mathworks.com>...
> On 11/10/2010 1:04 AM, Baha Kuzu wrote:
> > For an asymptotic function;
>
> doc fzero
>
> Alan Weiss
> MATLAB mathematical toolbox documentation

Subject: roots of an asymptotic function

From: Torsten Hennig

Date: 10 Nov, 2010 15:02:56

Message: 4 of 5

> Thank you Alan,
>
> But "fzero" is for the root if you know a close
> number to it, right? If so, how can I find let's say
> 30 roots or 50 roots? Can I still use fzero?
>
>
> Alan Weiss <aweiss@mathworks.com> wrote in message
> <ibe6hr$ile$2@fred.mathworks.com>...
> > On 11/10/2010 1:04 AM, Baha Kuzu wrote:
> > > For an asymptotic function;
> >
> > doc fzero
> >
> > Alan Weiss
> > MATLAB mathematical toolbox documentation

Start with a value x0 and calculate f(x0).
Set x = x + deltax until f(x) changes sign.
Compute the zero in between x and x-deltax
(e.g. by the method of nested intervals or
by a call to fzero).
Continue with x as the new starting point.
Set x = x + deltax ...
until you found as many zeros as you needed for
your task.

Best wishes
Torsten.

Subject: roots of an asymptotic function

From: Baha Kuzu

Date: 10 Nov, 2010 15:22:06

Message: 5 of 5

Thank you Torsten.

Actually I was thinking similar procedure, but I couldn't figure out how to write a script for it. Can you give me a simple example here how you find it?


> Start with a value x0 and calculate f(x0).
> Set x = x + deltax until f(x) changes sign.
> Compute the zero in between x and x-deltax
> (e.g. by the method of nested intervals or
> by a call to fzero).
> Continue with x as the new starting point.
> Set x = x + deltax ...
> until you found as many zeros as you needed for
> your task.
>
> Best wishes
> Torsten.

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