Chris
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 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.