3,588 reputation
12051
bio website regularize.wordpress.com
location Braunschweig, Germany
age 36
visits member for 4 years, 11 months
seen yesterday

Professor at TU Braunschweig.

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


Jan
8
comment Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$
Seems like I did not look careful enough on my mesh plot... Sorry.
Jan
8
comment Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$
Seems to be a bug in your numerics... Calculations look fine and my plots also...
Jan
8
answered Smoothing L1 norm, Huber vs Conjugate
Jan
8
comment Smoothing L1 norm, Huber vs Conjugate
Smoothing the dual will not give you a smooth primal. However, you get a strongly convex primal by dual smoothing (as opposed to merely a strictly convex primal by Huber smoothing). Hence, it depends on what kind of regularity you are aiming at: A smoother primal or a "more convex" primal - both can be helpful algorithmically. Moreover, note that there are numerous methods to treat nonsmooth convex minimization problems efficiently.
Jan
5
revised New grand projects in contemporary math
Extended description.
Jan
2
answered New grand projects in contemporary math
Dec
17
comment Most memorable titles
Reminds my of books with titles like "Theory of normal families". I've been told that one of these could be found in the "social sciences" section the university library in Bremen...
Dec
9
comment How to solve a system of linear equations without storing the matrix?
Granted, convergence can be slow (in terms of iteration count and computational effort - its advantage is low memory). You don't need any requirements for the matrix (for the complex case adjust the projection accordingly). In fact you could also apply the method to rectangular systems. It converges to some solution for the underdetermined case (and the minimum-norm solution if initialized with zero). In the overdetermined case you need to stop at some point as you'll see that the residual $\|AX-Y\|$ is not decreasing anymore.
Dec
7
answered How to solve a system of linear equations without storing the matrix?
Dec
7
answered If d/dx is an operator, on what does it operate?
Dec
5
answered ODE's without a Lipschitz condition
Nov
24
comment fixed point arguments in PDE
Would Schauder's fixed point theorem be standard or advanced?
Nov
14
comment Why is the Gaussian so pervasive in mathematics?
Isn't this connection the reason why the Gaussian is called Gaussian? If I remember correctly, Gauss introduced "least squares" as a regression technique not because its derivative gives rise to a linear problem but because the square fits the "normal error model", i.e. corresponds to the Gaussian distribution.
Nov
13
comment Weak convergence of the image of a weakly $L^1$ converging sequence
Not an answer, but I vaguely recall that the only functions $f$ for which $u_k$ weakly to $u$ implies $f(u_k)$ weakly to $f(u)$ are affine linear $f$'s.
Nov
5
awarded  Nice Answer
Nov
1
answered A sudden smiley? :-)
Oct
22
awarded  Popular Question
Oct
20
comment Inversion of Radon transform by incomplete data: specific case
Could you expand on the relation of the Radon transform and economics? (Out of curiosity.)
Oct
19
comment What software one needs to solve a big linear system on a small computer?
I also recommend octave. 10000 x 10000 is doable, although the matrix needs 800MB (if not sparse). On my laptop it takes about a minute to solve a system like this.
Oct
16
comment Measuring almost-critical values of smooth functions.
Did you inspect the one-dimensional case $X=\mathbb{R}$? I suspect that basically arbitrary functions $M_f$ are possible.