Thank you Izhak,
Cirip


"Izhak" <bucher@technion.ac.il> wrote in message
news:c52mpq$fc$1@news.iucc.ac.il...
> Cirip,
>
>    Numerical integration (cumsum) cannot guarantee absolute accuracy.
> There are more accurate schemes (cumtrapz),
> to enhance the accuracy  Increase the sampling rate.
>
>  Here are two examples
>
>
> dt=1/1000; wt=linspace(0,10,10/dt)';   y=cos(wt); yi1=cumsum(y)*dt ;
> yi2=cumtrapz(y)*dt; plot([sin(wt)-yi1 sin(wt)-yi2]);
> legend('cumsum-error','trapez-error')
>
>
> % use interpolation
>
> dt2=1/10000;                            % fine grid
> wt2=linspace(0,10,10/dt2)';    % prepare grid
> yI=spline(wt,y,wt2);                  % interpolate
> yi3=cumtrapz(yI)*dt2;              % integrate on finner grid
> plot(wt,[sin(wt)-yi1 sin(wt)-yi2],wt2,sin(wt2)-yi3 );  % compare
>
>
> HTH
> --
> izhak
>
> "cirip" <cirip@NOT_VALID.com> wrote in message
> news:wc4dc.15651$JTG1.14466@news04.bloor.is.net.cable.rogers.com...
> > Hello All,
> >
> > I believe a lot of the people on this ng are users of Matlab and heavily
> > into mathematics, so here is my question.
> >
> > I am trying to integrate a cosine function. If I compare the analitical
> > formula result with the numerical integration result using cumsum(),
there
> > is a small difference. Is there anything I can do to minimize that
> > difference, ideally make it zero?
> >
> > Unfortunately, using another integration method is not an option in my
> case.
> >
> > I can come back with more details if required.
> >
> > Thank you,
> > Cirip
> >
> >
>
>

Cirip,

   Numerical integration (cumsum) cannot guarantee absolute accuracy.
There are more accurate schemes (cumtrapz),
to enhance the accuracy  Increase the sampling rate.

 Here are two examples


dt=1/1000; wt=linspace(0,10,10/dt)';   y=cos(wt); yi1=cumsum(y)*dt ;
yi2=cumtrapz(y)*dt; plot([sin(wt)-yi1 sin(wt)-yi2]);
legend('cumsum-error','trapez-error')


% use interpolation

dt2=1/10000;                            % fine grid
wt2=linspace(0,10,10/dt2)';    % prepare grid
yI=spline(wt,y,wt2);                  % interpolate
yi3=cumtrapz(yI)*dt2;              % integrate on finner grid
plot(wt,[sin(wt)-yi1 sin(wt)-yi2],wt2,sin(wt2)-yi3 );  % compare


HTH
-- 
izhak

"cirip" <cirip@NOT_VALID.com> wrote in message
news:wc4dc.15651$JTG1.14466@news04.bloor.is.net.cable.rogers.com...
> Hello All,
>
> I believe a lot of the people on this ng are users of Matlab and heavily
> into mathematics, so here is my question.
>
> I am trying to integrate a cosine function. If I compare the analitical
> formula result with the numerical integration result using cumsum(), there
> is a small difference. Is there anything I can do to minimize that
> difference, ideally make it zero?
>
> Unfortunately, using another integration method is not an option in my
case.
>
> I can come back with more details if required.
>
> Thank you,
> Cirip
>
>

Hello All,

I believe a lot of the people on this ng are users of Matlab and heavily
into mathematics, so here is my question.

I am trying to integrate a cosine function. If I compare the analitical
formula result with the numerical integration result using cumsum(), there
is a small difference. Is there anything I can do to minimize that
difference, ideally make it zero?

Unfortunately, using another integration method is not an option in my case.

I can come back with more details if required.

Thank you,
Cirip