bio | website | regularize.wordpress.com |
---|---|---|
location | Braunschweig, Germany | |
age | 36 | |
visits | member for | 4 years, 2 months |
seen | 16 hours ago | |
stats | profile views | 1,784 |
Professor at TU Braunschweig.
Area: Inverse problems, regularization theory, applied functional analysis, mathematical image processing.
Nov 4 |
comment |
Polynomials with prescribed points to match prescribed bounds
Oh, there is a simpler argument: Since there are piecewise monotone interpolating polynomials we can use them directly to interpolate the $x^+$ and $x^-$ (and possibly adding zero interpolation points inbetween). |
Nov 4 |
comment |
Polynomials with prescribed points to match prescribed bounds
Such a polynomial always exists: Take a Chebycheff polynomial $P$ of degree high enough (such that is attains the values 1 and -1 in the right order at point $t_i$. Then choose a monotone polynomial $Q$ which maps the points $t_i$ to the prescribed $x_i$ and take $P\circ Q$. Such monotone polynomial interpolants exit by a theorem of Young (ams.org/mathscinet-getitem?mr=0212455). |
Nov 3 |
comment |
Polynomials with prescribed points to match prescribed bounds
That is pretty clear. I am willing to add more assumptions and not hoping for a very clean answer. |
Nov 3 |
asked | Polynomials with prescribed points to match prescribed bounds |
Oct 27 |
comment |
Find vector in R^n which is orthogonal to given (n-1) vectors v_i under condition v_i are orthonormal.
Look at this en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process |
Oct 23 |
comment |
Low degree polynomial approximation for the entropy function
It would also be good to know what "good" means in your context. Uniform approximation? Mean squared? Or even Kullback-Leibler? |
Oct 17 |
comment |
What is the maximum diameter of $N$ steps of a random walk?
Thanks! Probably I should note that also the expected value would be helpful. |
Oct 14 |
comment |
What is the maximum diameter of $N$ steps of a random walk?
@cardinal: Bounds would also be helpful as well as asymptotic results. I briefly went over the papers you linked - as I understood thay all rely in some way on the ordering of the reals and hence, generalization seems not to be straightforward... |
Oct 14 |
comment |
What is the maximum diameter of $N$ steps of a random walk?
Thanks so far for the comments and references! I'll check them out. @Igor: Is this also called Brownian motion if it is time discrete? Would it be right to say that the time discrete model is a sampled continuous Brownian motion? Sorry for my ignorance on this topic... |
Oct 13 |
asked | What is the maximum diameter of $N$ steps of a random walk? |
Oct 12 |
comment |
Best Poincare constants on the surface of a ball
Are there any such maps $\xi$ in the case of $\mathbb{R}^2$ which are in $H^1$? |
Oct 7 |
comment |
Fast root finding for strictly decreasing function
How fast? Is the derivative available? What is wrong with bisection? |
Sep 30 |
awarded | Yearling |
Sep 26 |
comment |
One-line proof of the Euler's reflection formula
Could a down-to-earth proof have one line? |
Sep 20 |
comment |
Do you know this form of an uncertainty principle?
I got a little bit confused with all these different inequalities around (many of them called Caffarelli-Kohn-Nirenberg) but now I see. That's an interesting relation though. The Heisenberg uncertainty is also included? ($\gamma=\alpha=0$, $\beta=−1$, $a=1/2$) |
Sep 20 |
comment |
Do you know this form of an uncertainty principle?
Wow, there are lot of constants involved. As far as I've seen, it seems that the case $\gamma=0$, $a=1$ and $\alpha=-1$ is not included? |
Sep 20 |
asked | Do you know this form of an uncertainty principle? |
Sep 19 |
comment |
Decomposing max-convolution of sum of functions ?
Sorry, I do not get several points: What are $x$, $y$, $dx$ and $dy$? What are the $d_i$'s? What do you mean by "random" matrices (especially in the light that they seem to depend on $x$ and $y$)? |
Sep 12 |
comment |
Unique limits of sequences plus what implies Hausdorff?
Thanks! Especially the topospaces.subwiki.org is pretty cool... |
Sep 7 |
revised |
When does symmetry in an optimization problem imply that all variables are equal at optimality?
Corrected wording |