3,037 reputation
1247
bio website regularize.wordpress.com
location Braunschweig, Germany
age 36
visits member for 4 years
seen 1 min ago

Professor at TU Braunschweig.

Area: Inverse problems, regularization theory, applied functional analysis, mathematical image processing.


Oct
14
answered Selecting Rays for Simulated Radon Transform
Oct
14
reviewed Approve suggested edit on Two Equal Series?
Oct
13
comment Is this series well known?
Oops, totally missed that $!$…
Oct
13
comment Is this series well known?
Well, its only loosely related. Your f is almost the integral of $\sum t^{n^2}$…
Oct
13
comment Is this series well known?
Related to (integral of) the theta function $\theta(0,\tau)$, de.wikipedia.org/wiki/Thetafunktion.
Oct
9
comment Proofs without words
I find the underlying argument extremely nice but the picture (especially the animated one) does not really work for me without any words. The animation makes me think that is has some meaning that the yellow dots are visited in a certain order.
Oct
9
comment Why are the angular differences of these random complex polynomial coefficients almost constant?
Yeah sorry, I still had the question mathoverflow.net/questions/182412/… in mind. For roots in the unit square the effect I see is much smaller but still can be seen (still working with double precision floating points). I still tend to blame the random number generators; but this is far from my field and so this suspicion is not backed up…
Oct
9
answered Why are the angular differences of these random complex polynomial coefficients almost constant?
Oct
8
comment Can one always find sparse solutions to an $\ell^1$-minimization problem?
Question reformulated in terms of the optimality system: $x^*$ is an $\ell^1$-minimal solution if $Ax^*=b$ and there exists $w$ such that $A^T w \in\partial\|x\|_1$. This says: there is no $m$-sparse solution if the range of $A^T$ (which is $m$-dimensional) does not intersect the $m$-dimensional faces of the unit cube. Answers to this question show that for $m\geq n/2$ this can not happen. (Unfortunately, $m$ and $n$ are swapped in the linked question.)
Oct
8
comment Why do roots of polynomials tend to have absolute value close to 1?
This is really strange. My experiments with MATLAB (just with double precision floating points) show strange effects even when I calculate the coefficients of a polynomial which has $N$ roots precisely (up to eps) at the roots of unity when $N$ is as small as 100. I obtain a polynomial with very large coefficients for the middle exponents, and comparably small coefficients close $x^0$ and $x^N$.
Oct
8
comment Why do roots of polynomials tend to have absolute value close to 1?
I notice that this answer is close in spirit to the one by @tros443.
Oct
8
answered Why do roots of polynomials tend to have absolute value close to 1?
Oct
1
comment ellipsoids have spherical section
Capitalization and punctuation as well as consistent TeX would be helpful.
Sep
29
awarded  Yearling
Sep
29
comment What is the most useful non-existing object of your field?
I use the non-existence of a number that is both positive and negative much more often then the non-existence of a number that is less than and greater than $1$. However, the non-existence of a number that is both positive and negative follows easily: Let $x$ fulfill i) $x<1$ and ii) $x>1$. Then for $y = x-1$ we have by i) that $y<0$ and by ii) that $y>0$ and hence, $y$ has the desired properties. Since $x$ does not exist, $y$ also does not exist either.
Sep
24
comment A continuous function for defining unique values to a 1024x1024 image with a 24 bit 3 color channel image
Put differently: You look for an injective mapping $f:2^{10}\times 2^{10} \to 2^8\times 2^8\times 2^8$ which is Lipschitz continuous with constant 1 where we put the $1$-norm on $2^{10}\times 2^{10}$ and the $\infty$-norm on $2^8\times 2^8\times 2^8$.
Sep
23
comment Results true in a dimension and false for higher dimensions
I am curios to see this as a dimension phenomenon…
Sep
17
comment For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$?
So now the question is: For what measures $\mu$ does $\mu * f \in L^\infty$ hold, right?
Sep
12
comment How does the distribution of Erdős number evolve over time ? How to build a model to fit the real data ?
I suspect that the assumption that the Nummer of new articles and mathematicians is constant is false and guess that both grow superlinearly if not exponentially (at least for the next few years - eventually it may be logistical growth...).
Sep
11
comment Checking the intersection of two sets
Of course, you could also use @EmilJeřábek's formulation and use the constraints $l\leq Xy\leq u$.