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23h
comment Frankl's union-closed sets conjecture for infinite families
Sorry for my ignorance, but why the down vote?
1d
comment Relation between eigenvalues of $A$ and $A^TA$?
I was under the impression that you had in mind to make the matrix $A$ "numerically better" by adding $cI$. My remark should only point out that it's not that simple.
Feb
3
comment Relation between eigenvalues of $A$ and $A^TA$?
Are you aware that for $A = [0\ 1;1\ 0]$ it holds $\kappa(A) = 1$ but $\kappa(A+I) = \infty$?
Jan
29
comment Nuclear norm maximization
You should hope for too much: The orthogonality constraint is not linear and not even convex and also you are maximizing instead of minimizing. So your problem is in a very different realm of problems than the one where you want to go.
Jan
26
comment What's the relationship between the roots of a function and that of a filtered Fourier series representation?
Isn't your $M$ a linear combination of "unit step functions"/"square waves"? Since Fourier coefficients are linear, your truncated Fourier series is a linear combination of truncated Fourier series squares waves. At every step you get some Gibbs phenomenon and these add up. Do you expect anything more than that?
Jan
26
comment Is finding a local minimizer of a NP-hard optimization problem is still NP-hard
Now you have two contradicting answers that answer slightly but crucially different interpretations of your question.
Jan
26
comment Is finding a local minimizer of a NP-hard optimization problem is still NP-hard
I find this question much too vague and vote to close until it's phrased more carefully . First, not all problems are optimization problems, hence, asking for a "local minimizer of an NP-hard problem" does not make sense. Second, "NP-hardness" is not a property of some problem, but of some problem class. Third, it may well be that for some problem class global minimizers are hard to find while local minimizers aren't, but for some other problem class its different. Or are you looking for a specific result telling that "if global minimizers are NP-hard to find, then local minimizers too"?
Jan
22
comment state-of-art numerical contour (complex) integration method when contour is square and available values are evenly spaced
@CarloBeenakker Is this state of the art? Also, I would find it more comfortable if the link would point to some page where I can find authors, abstract, journal and so forth to decide whether I want to download a pdf. (In fact, one can deduce the journal, year and probably issue from the url but that's not that convenient.)
Jan
18
comment Reference Request: Variational Problem
Since there are relevant comments here and at scicomp I suggest that the this question should be migrated to scicomp and there marked as a duplicate of the other.
Jan
18
answered Reference Request: Variational Problem
Jan
18
comment Question on solving an optimization problem using Variable splitting and ADMM
Will ADMM and variable splitting solve this? I think you have to try this to get an answer. (Implementation seems straightforward and monitoring descent of the objective also. Checking second order sufficient conditions seems also possible…)
Jan
15
comment Is the Fourier transform of $e^{-|x|^n}$ positive?
I guess $|x|$ is the euclidean norm in n dimensions...
Jan
15
comment Is the Fourier transform of $e^{-|x|^n}$ positive?
Not sure if you answered the right question. Note that dimension of the domain is also $n$.
Jan
15
comment Question on solving an optimization problem using Variable splitting and ADMM
ADMM would builde the augmented Lagrangian for the problem and then alternatingly minimize between $v$ and $x$ with suitable update for the Lagrange multiplier. You may get intro trouble due to the nonlinear (in fact bilinear) constraint for $x$ (which I interpret componentwise, right?) resulting in a non-convex subproblem for the $x$ minimization (and also no convergence result I knows will be applicable).
Jan
15
comment Can we simplify $\int_{0}^{\infty}\frac{{\sin}^px}{x^q}dx$?
This purpose of this comment is to make you aware that I see [Math Processing Error]s here.
Jan
14
comment Interpret Fourier transform as limit of Fourier series
If the Fourier transform of f has compact support, then f is not compactly supported (follows from Heisenberg uncertainty principle, or, more nicely from the uncertainty principle by Donoho and Stark). Hence, there are countable many nonzero samples that determine f completely. If bandlimited functions could be compactly supported, signal processing would be considerably much easier.
Jan
14
comment Interpret Fourier transform as limit of Fourier series
Interpreting Fourier inversion as a limit is not only interpreting but is the right way to see Fourier inversion in $L^2$. One defines the Fourier transform by extending it from Schwartz space (or $L^1\cap L^2$) to $L^2$ and similar for the inverse. To be concrete one can use the limit $\lim_{T\to\infty} \int_{-T}^T \hat f(\xi) \exp(i x\xi) d\xi$…
Jan
7
reviewed Approve Has anyone studied a transport equation of this form?
Jan
7
comment How to cite authors from any country correctly?
@FedericoPoloni That's well said. In view of the answers and the comments a migration, this thread would probably appear a bit odd at academia.sx. I retracted my close vote…
Jan
6
comment How to cite authors from any country correctly?
As suspected: ResearchGate and Google Scholar also have the wrong name while MathSciNet has this correct…