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seen Jan 21 '13 at 12:17

Aug
18
comment Equation - Basic operations on matrices
Perfect, thank you!
Aug
18
comment GMRES algorithm
Thank you timur!
Aug
18
comment GMRES algorithm
Thank you, will look into all the posted resources and report back.
Aug
17
comment Book on constrained numerical optimization
Any news on this J.M. ? :)
Jul
24
comment Laurent series - $f(z)=\frac{1}{z^2-4}+\frac{1}{6-z}$
Thank you very much!
Jul
24
comment Laurent series - $f(z)=\frac{1}{z^2-4}+\frac{1}{6-z}$
Alright, thank you!
Jul
24
comment Laurent series of $f(z)=\frac{1}{z(z-1)(z-2)}.$
Great, things are much clearer now. I was until now utterly confused about that!
Jul
24
comment Laurent series of $f(z)=\frac{1}{z(z-1)(z-2)}.$
That's very good robjohn, thank you so much! Question on point 3: In my case, there are no negative powers of $z-0$, doesn't this fact change something? Do we still have a Laurent series, even if all powers are positive ($k$ starts at $0$ in both cases)
Jul
24
comment Laurent series - $f(z)=\frac{1}{z^2-4}+\frac{1}{6-z}$
I've added the missing information. So we don't do anything with $\frac{1}{z-2}$, because it's already part of the expansion around z=2 and there is nothing additional to be done here, right?
Jul
24
comment Laurent series - $f(z)=\frac{1}{z^2-4}+\frac{1}{6-z}$
Some exercise notes from a complex analysis course I attended.
Jul
23
comment Complex contour integral
"it cannot apply to this case as we only have one quarter of a circumference" - because $t \in \left[0,\frac{\pi}{2}\right]$?
Jul
23
comment Complex contour integral
Could you elaborate your question, I am not sure in which direction you are pointing...
Jul
23
comment Evaluating $\int_{|z|=1} \frac{\sin(z^2)}{ \left( \sin(z) \right)^2} dz.$
Thank you very much!
Jul
23
comment Evaluating $\int_{|z|=1} \frac{\sin(z^2)}{ \left( \sin(z) \right)^2} dz.$
The residue theorem?
Jul
23
comment Evaluating $\int_\gamma \frac{\cos(z)}{z^3+2z^2} \ dz$
So we have $f'(0)=-\frac{1}{4}$ and $\int_\gamma \frac{\cos(z)}{z^3+2z^2} dz=-\frac{1}{2}\pi i$. Thank you very much!
Jul
23
comment Evaluating $ \int_{|z|=1} \frac{e^z}{(z+3)\sin(2z)} \ dz$
It's a removable singularity. So we could look at $\lim_{z\rightarrow 0} f(z) = \frac{1}{6}$. Do we now set $f(0)=\frac{1}{6}$ and carry on with the Cauchy integral formula? What would have happened if the singularity wasn't removable or if we had multiple singularities?
Jul
23
comment Evaluating $\int_{-\pi}^{\pi} \cos(e^{it})dt$
Oh, I see, so we have a path $\gamma:[-\pi,\pi]\rightarrow\mathbb{C}$, $\gamma(t)=e^{it}$ and we can rewrite it as: $\frac{1}{i}\int_{\gamma}\frac{cos(z)}{z}dz$ and use Cauchy's integral formula.
Jul
23
comment Integral over circle
I see, so the integral is zero using the Cauchy integral theorem.
Jul
22
comment Trust Region Method
You are right. I'll rephrase: if we have the case that $||p||=\Delta$, what does this mean?
Jul
22
comment Minimization of function with large dimensions
I don't have any details on the form of $f$. I was just wondering if there are some preferred algorithms when you have functions of high dimensions. It's not a specific question about something particular, I was just wondering.