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Dec
18
answered Projection onto rotated box
Dec
10
revised Parametrised Hilbert spaces; can we put a norm on the following space of Hilbert spaces?
added 216 characters in body
Dec
10
comment Parametrised Hilbert spaces; can we put a norm on the following space of Hilbert spaces?
@JochenWengenroth Right! Not particularly help notion here…
Dec
10
answered Parametrised Hilbert spaces; can we put a norm on the following space of Hilbert spaces?
Dec
2
comment Correlation of Fourier transforms of characteristic functions
Reminds me a bit of the uncertainty principle of Donoho and Stark.
Nov
30
revised Moreau-Yosida regularization in Banach spaces
fixed typo and added link.
Nov
30
comment Moreau-Yosida regularization in Banach spaces
It does not hold that $F(x_i,y_i) \leq f(x_i)$.
Nov
26
answered Moreau-Yosida regularization in Banach spaces
Nov
20
answered Probability for a random positive-semidefinite matrix to not be positive-definite?
Nov
19
comment Probability for a random positive-semidefinite matrix to not be positive-definite?
This is really a comment (i.e. a pointer to an answer) rather than an answer.
Nov
15
comment Continuity of minimizer of a function with respect to another variable
This is not easy in general. Convexity of $g$ and $h$ is helpful (while differentiability is not that important).
Nov
13
answered Notions of convergence not corresponding to topologies
Nov
12
comment Wasserstein distance, convex polytopes and extreme points
You should also state the metric on $\mathbb{R}^d$ you use (presumably the euclidean metric).
Nov
9
comment Iterated projections in Hilbert spaces
Also the case of subspaces replaced by convex sets (and also with more than two of them) is well studied. Buzzwords are "POCS" (projections onto convex sets), alternating projection method, von Neumann's alternating projection algorithm. In case of closed set you get at least weak convergence but probably that is not the case you are interested in?
Nov
7
answered Choosing the order of Tikhonov regularization of an inverse problem
Nov
7
comment Choosing the order of Tikhonov regularization of an inverse problem
Just to nit-pick a bit: For sure you have some information (or at least intuition) about $b$: If not, why isn't $b = M^{-1} a$ (or $b=M^\dagger b$ if $M$ is not invertible) an acceptable solution? Of course you know, that $M$ is very ill-conditioned and hence, noise if $a$ would be amplified very much, but still: Without any assumptions on $b$, that would be a valid solution.
Nov
7
comment Size of KL-divergence neighbourhoods
Note that Pinsker's inequality bounds KL from below by the square of the total variation distance. This gives a bound which is similar for $\mathbf{P}$ and $\mathbf{Q}$.
Nov
6
comment Do interpolation nodes have to be dense?
I am not sure how this answers the question. First, the question specifically considers $f=\exp$ and second I am not sure if multiplicity of the interpolation points was allowed by the OP.
Oct
31
comment Eigenvalue computation using inverse iteration
Why do you need to use inverse iteration: en.wikipedia.org/wiki/…
Oct
28
comment Question on convex optimization and dual norms
To speak of polar functions, don't you need that the functions are positively homogeneous?