Gabriel Landi
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 Jan14 comment Average distance between random points inside a cube Oh! Yeah, I think that is it. The nearest-neighbour distance. I got everything confused. Jan14 comment Average distance between random points inside a cube I am still confused about where the concentration of points enter. I mean, if $n$ is large, than the average distance between them should be smaller, but I don't see how that enters the calculation. Anyway, thank you for the help. Nov29 comment Solving for the trace of a matrix This is incredible. Thank you so very very much. Nov27 comment Solving for the trace of a matrix I have come across that manipulation but, unfortunately, it does not remove $\Theta$ so it doesn't really work much. But, in any case, thanks for your help. Nov27 comment Solving for the trace of a matrix @Berci the matrix $\Theta$ is uniquely determined from the Lyapunov equation. Hence so is $F$. Nov17 comment Reference suggestion: eigenvalues of tridiagonal matrices @Elias Great. Thank you very much. Sep10 comment Discrete Analogue of the Fundamental Theorem of Calculus Good Point. :) Once again, thank you. Sep10 comment Discrete Analogue of the Fundamental Theorem of Calculus I see. But isn't this notation misleading? I mean, in continuous calculus you write $d/dx$ to specify the derivative is with respect to $x$. Wouldn't $\Delta_n$ be a more adequate notation? And is this common in difference calculus literature? Anyway, thank you very much for the answer. Aug31 comment Modification of the continuous time Lyapunov Equation The idea in your answer is probably unfeasible, since my system has $n > 200$. Could you point out a reference for this pole-place method? By the way, thanks for the support. Aug21 comment Calculate a whitening matrix without using inverses? Isn't computing the entire eigenvector matrix also expensive, even for a symmetric matrix? I wonder if Cholesky itself isn't faster. Aug14 comment Solving for specific entries in a Lyapunov Equation Actually, I have been looking at the web and haven't yet found a method for solving the eq. for B. Any ideas on where to look? Aug14 comment Solving for specific entries in a Lyapunov Equation Wow, this is great. Thank you! I'll start testing this idea right away and post some results as soon as they come out. Aug9 comment Solving for specific entries in a Lyapunov Equation @dato, Sorry I don't understand. Aug9 comment Solving for specific entries in a Lyapunov Equation The solution of the Lyapunov equation, $R$, will be symmetric and positive definite (it is actually a covariance matrix). What I can prove is that $C$ is anti-symmetric ($C^\text{T} = -C$) Jul28 comment Partial Fractions Expansion of $\tanh(z)/z$ Yeah. Probably. Hehe. It's just that I never know how to deal with sums in any other way than comparing it to other sums. Again, thank you for the answer J.M. Jul28 comment Partial Fractions Expansion of $\tanh(z)/z$ @jm this is great; does all such formulas rely on manipulating other known products and sums? Isn't there, for instance, a Fourier transform or generating function approach (or something...)? Again, thank you for the support. Jul27 comment Approximate solution for the root of a non-linear function Let $F_\pm(t) = e^t (g \cos(\omega t-\phi) \pm b)$. The first point, $t_0$ say, is computed from either $F_\pm(t_0) = F(0) \mp \alpha$, where $\alpha$ is a positive constant. From there one the roots are computed sequentially as above. Jul27 comment Approximate solution for the root of a non-linear function Thank you all very much for the support and thank you @LeonidKovalev for the bounty. Jul26 comment Approximate solution for the root of a non-linear function Yes Mr. Badwaik. I want the first $t_1$ after $t_0$. Jul25 comment Distance between discrete random variables Mr. Schmuland, thank you for your answer Indeed, I was interpreting $Y$ as signifying the G's in your answer, thinking they could all be treated as a single variable. Is that impossible? This confuses me: suppose I take the limit of both $n$ and $k$ going to $\infty$, but such that k/n remains fixed. Then $Y$ represents E(G's)? Thank you again for your time.