Numerical Analysis: Inverse Problems—Theory and Applications, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 31 March 2024 | Viewed by 1798

Special Issue Editor

Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam OT Golm, Germany
Interests: numerical and applied mathematics; linear and nonlinear inverse ill-posed problems; regularization methods; numerical methods for inverse Sturm-Liouville problems; applications in atmospheric physics
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Special Issue Information

Dear Colleagues,

This Special Issue, “Numerical Analysis: Inverse Problems—Theory and Applications”, will be open for the publication of high-quality mathematical papers in the area of linear and nonlinear inverse ill-posed and well-posed problems.

Plenty of problems in mathematics, economics, physics, biology, chemistry, and engineering, e.g., optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, non-destructive testing, and other disciplines, can be reduced to solving an inverse problem in an abstract space, e.g., in Hilbert and Banach spaces. Inverse problems are called that because they start with the results and then calculate the causes. Solving inverse problems is a non-trivial task that involves many areas of Mathematics and Techniques. In cases where the problem is ill-posed, small errors in the data are greatly amplified in the solution, and therefore, regularization techniques using parameter choice rules with optimal convergence rates are necessary.

While inverse problems are often formulated in infinite dimensional spaces, limitations to a finite number of often noisy data, and the practical consideration of recovering only a finite number of unknown parameters, may lead to the problems being recast in discrete form. In this case, the inverse problem will typically be ill-conditioned.

Papers involving all those abovementioned topics are welcome. Moreover, this Special Issue offers an opportunity to researchers and practitioners to communicate their ideas.

Prof. Dr. Christine Böckmann
Guest Editor

Manuscript Submission Information

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Keywords

  • Inverse problems
  • Ill- and well-posed problems
  • Regularization
  • Inverse Sturm-Liouville problems

Published Papers (1 paper)

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Research

18 pages, 326 KiB  
Article
Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space
by Dijana Mosić, Predrag S. Stanimirović and Spyridon D. Mourtas
Mathematics 2023, 11(7), 1732; https://doi.org/10.3390/math11071732 - 05 Apr 2023
Cited by 2 | Viewed by 882
Abstract
The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems. The main novelty of this paper is the unification of solutions of considered matrix equations with corresponding minimization problems. For a [...] Read more.
The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems. The main novelty of this paper is the unification of solutions of considered matrix equations with corresponding minimization problems. For a particular case we extend some well-known results and give several new results for the weak Drazin inverse. The main characterizations of the Drazin inverse, group inverse and Moore–Penrose inverse are obtained as consequences. Full article
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