Dirk
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Registered User
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Assistant professor at TU Braunschweig.
Area: Inverse problems, regularization theory, applied functional analysis, mathematical image processing.
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1d |
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Approximating higher dimension step function Mollifier are a tool of real analysis of often used in functional analysis: en.wikipedia.org/wiki/Mollifier And you are right that convolution with a mollifier is a low-pass filter. |
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1d |
revised |
Approximating higher dimension step function added 36 characters in body |
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1d |
answered | Discretizing a cosine function? |
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1d |
answered | Approximating higher dimension step function |
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Apr 10 |
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Image of L^1 under the Fourier Transform Ah, I see. Interesting that the Wikipedia pages of the Wiener algebra and the Fourier algebra do not mention each other... |
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Apr 9 |
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Image of L^1 under the Fourier Transform Isn't this space related to the Wiener Algebra? This is the space of $2\pi$-periodic functions with absolute summable Fourier coefficients. I vaguely remember that I heard somebody calling the image of $L^1$ under Fourier transform also "Wiener Algebra"... |
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Mar 27 |
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any standard numerical methods for integral equations? For other types, you may consult Hackbusch's "Integral equations: Theory and numerical treatment". |
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Mar 27 |
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any standard numerical methods for integral equations? If your equation is Fredholm of the first kind and your equation is ill-posed you may look into "The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind" by Chuck Groetsch. |
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Mar 26 |
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Application and relevance of Sobolev gradients The link seems broken. |
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Mar 21 |
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“Wild” solutions of the heat equation: how to graph them? Thanks!$\mbox{}$ |
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Mar 21 |
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“Wild” solutions of the heat equation: how to graph them? Corrected exponent |
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Mar 21 |
answered | “Wild” solutions of the heat equation: how to graph them? |
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Mar 1 |
answered | Modern developments in finite-dimensional linear algebra |
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Feb 19 |
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Fiction books about mathematicians? Here: mathoverflow.net/questions/101644/… |
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Feb 12 |
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2-Wasserstein (optimal transport) and extension to the set of all signed measures Related question: mathoverflow.net/questions/120291/… |
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Feb 7 |
answered | Why is Set, and not Rel, so ubiquitous in mathematics? |
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Feb 6 |
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Metrization of weak convergence of signed measures That is in the direction I was thinking. I just found a similar construction in Gromov's "Metric structures" chapter $3\tfrac{1}{2}$.B: For any metric $d$ defined for measures of the same total mass one may define a metric for all finite measures as follows. The distance between two measures $\mu$ and $\nu$ with total masses $\mu(\Omega) = m$ and $\nu(\Omega)=n$ with $n>m$ define $D(\mu,\nu) = n-m + d(\mu,\tfrac{m}{n}\nu)$ (and the distance to infinite measures is just $\infty$). Apparently, this definition also works for metric measure spaces. |
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Feb 4 |
revised |
Metrization of weak convergence of signed measures added 250 characters in body |
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Jan 30 |
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Metrization of weak convergence of signed measures Thanks a lot for the enlightening answers so far! Since I am off for a long weekend, I will have a closer look in a few days. |
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Jan 30 |
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Metrization of weak convergence of signed measures Indeed, I wanted metric spaces - question edited. Thanks for pointing this out. |
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Jan 30 |
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Metrization of weak convergence of signed measures Changed setup from Hausdorff to metric spaces. |
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Jan 30 |
asked | Metrization of weak convergence of signed measures |
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Jan 29 |
answered | Journals for undergraduates |
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Jan 25 |
answered | Quantitative Version of Jensen’s Inequality? |
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Jan 25 |
answered | Kronecker-structured matrix kernel |
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Jan 24 |
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Kronecker-structured matrix kernel Isn't the relation $vec(ABC) = (C^T \otimes A) vec(B)$ helpful? |
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Jan 24 |
awarded | ● Good Answer |
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Jan 18 |
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“Harmonacci” recurrence and identities for $\pi$ +1 for "Harmonacci" |
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Jan 15 |
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Some career start-up (postdoc) questions Better suited for academia.stackexchange.com, I think. Moreover, I do not know what a TT job is, neither what named postdoc positions are and what XYZ V.A.P or VAP could mean. |
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Jan 9 |
accepted | Elaborating Mercer’s theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$ |
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Jan 9 |
answered | Elaborating Mercer’s theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$ |
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Jan 9 |
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Smoothing L1 norm, Huber vs Conjugate I don't think so - I even think that a dual solution does not always give you a way to infer a primal solution... (regardless of smoothing). Probably an answer can be found in Nesterov's "Smooth minimization of non-smooth problems". |
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Jan 8 |
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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. |
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Jan 8 |
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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... |
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Jan 8 |
accepted | Smoothing L1 norm, Huber vs Conjugate |
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Jan 8 |
answered | Smoothing L1 norm, Huber vs Conjugate |
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Jan 8 |
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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. |
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Jan 5 |
revised |
New grand projects in contemporary math Extended description. |
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Jan 2 |
answered | New grand projects in contemporary math |
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Dec 17 |
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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... |
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Dec 9 |
accepted | How to solve a system of linear equations without storing the matrix? |
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Dec 9 |
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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. |
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Dec 7 |
answered | How to solve a system of linear equations without storing the matrix? |
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Dec 7 |
answered | If d/dx is an operator, on what does it operate? |
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Dec 5 |
answered | ODE’s without a Lipschitz condition |
