[Turkmath:5825] Re: (no subject)

Fri Nov 11 06:28:48 UTC 2022

Dear Colleagues!

You are cordially invited to the Weekly Online Seminar “Analysis and
Applied Mathematics” on

Date: Tuesday, November 15, 2022

Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 17.00-18.00 (Almaty)

Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09,
Conference ID: 667 827 0445, Access code: 1

Speaker: Prof. Dr. Fadi Awawdeh
The Hashemite University, Jordan
  Title:  Regularization of Ill-Posed Inverse Problems
Abstract:  Ill-posed inverse problems are at the core of many challenging
applications in the natural sciences, medicine and life sciences, as well
as in engineering and industrial applications. The talk illustrates the
potential difficulties with reversing the process; namely, given a measured
state of the model, try to determine what exact equation could have
produced this outcome.
 We will primarily consider operator equations Au = y, with the operator A : E
 Y  mapping between function spaces E and Y . We assume that the operator
equation is ill-posed in the sense that small perturbations of y can lead
to arbitrarily large perturbations on u (or even lead to non-existence of a
solution). To obtain a stable estimate of the solution of such problems, it
is often necessary to implement a regularization strategy. This requires the
solution approach to satisfy some regularizing properties,i.e., be stable
even for noisy data yб with  yб — y  ≤ б in place of y and yield
reconstructions yб that converge to the exact solution u† as б          0.
Regularization techniques are the subject of this talk and we will attempt
to highlight two approaches that are wide-spread in the literature:
(i) Variational methods are based on minimizing a weighted sum of a
discrepancy term and a suitable regularization term (Tikhonov
regularization) or on minimizing one of these terms under a constraint on the
other (Ivanov or Morozov regularization, respectively);
(ii) Iterative methods construct a sequence of iterates approximating the
solution u†.

Keywords— Regularization, Ill-posed Problems, Variational Methods, Iterative
Methods

References

[1]    Hofmann, B., Kaltenbacher, B., Pöschl, C., Scherzer, O. 2007: A
convergence rate result for Tikhonov regularization in Banach spaces with
non-smooth operators. Inverse Problems, 23(3) 987–1010.

[2]    Kaltenbacher, B., Neubauer, A., Scherzer, O. 2008: Iterative
Regularization Methods for Nonlinear Ill-Posed Problems. Radon Series on
Computational and Applied Mathematics. de Gruyter, Berlin, 2008.

[3]    Kaltenbacher, B., Rundell, W. 2019: Regularization of a backwards
parabolic equation by fractional operators. Inverse Problems and Imaging,
(13) 401–430.

[4]    Werner, F. 2015: On convergence rates for iteratively regularized
Newton-type methods under a Lipschitz Type  nonlinearity condition. Journal
of Inverse and ILL-posed Problems, (23) 75–84.
Abstracts and forthcoming talks can be found on our webpage
https://sites.google.com/view/aam-seminars

Kind regards,
*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University, 34353, Istanbul, Turkey*
*  and **Near East University, Lefkoşa(Nicosia), Mersin 10 Turkey*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at eng.bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars
https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml
*icaam-online.org <http://icaam-online.org>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*

On Thu, 2 Jun 2022 at 16:13, Allaberen Ashyralyev <
Allaberen.Ashyralyev at listweb.bilkent.edu.tr> wrote:

> Dear Colleagues!
>
> You are cordially invited to the Weekly Online Seminar “Analysis and
> Applied Mathematics” on
>
> Date: Tuesday, June 07, 2022
>
> Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 17.00-18.00 (Almaty)
>
> Zoom link:
> https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09,
> Conference ID: 667 827 0445, Access code: 1
>
> Speaker: Prof. Dr. Yusif Gasimov
>  Azerbaijan University, Baku, Azerbaijan
>  Title: In this talk an inverse spectral problem is considered with
> respect to the domain for the Schrödinger equation. Using the introduced
> space of the pairs of the convex domains a new definition of the domain
> variation is given. The first variation of the eigenvalues with respect to
> domain is calculated, a new formula for the eigenvalues of the Schrödinger
> operator is proved. A definition of s-function is introduced and a scheme
> is proposed to reconstruct the domain by the given set of the s-functions.
> Some particular cases are also considered.
>
> Abstracts and forthcoming talks can be found on our webpage
> https://sites.google.com/view/aam-seminars
>
> Kind regards,
> *Prof. Dr. Allaberen Ashyralyev *
> *Department of Mathematics, Bahcesehir University, 34353, Istanbul, Turkey*
> *  and **Near East University, Lefkoşa(Nicosia), Mersin 10 Turkey*
> *Peoples' Friendship University of Russia (RUDN University),** Ul
> Miklukho Maklaya 6, Moscow 117198, Russian Federation *
> *Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
> Kazakhstan*
> *e-mail: allaberen.ashyralyev at eng.bau.edu.tr
> <allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
> <aallaberen at gmail.com> *
>  http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev
>
> https://sites.google.com/view/aam-seminars
> https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml
> *icaam-online.org <http://icaam-online.org>*
>
> *https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
> <https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
> _______________________________________________
> Turkmath mailing list
> Turkmath at listweb.bilkent.edu.tr
> http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/listinfo/turkmath
>
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