New Advances in Numerical Linear Algebra and Its Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1316

Special Issue Editor


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Guest Editor
Department of Engineering Sciences, Bulgarian Academy of Sciences, 1040 Sofia, Bulgaria
Interests: matrix computations; control theory; robust control; numerical methods; software for matrix computations and control system design
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Special Issue Information

Dear Colleagues,

Numerical Linear Algebra is the basis of Numerical Analysis. All numerical algorithms involve elements related to the solution of linear systems, linear least squares problems or eigenvalue and singular-value computations. Since this is an area of active research, new ideas and applications are constantly emerging. Therefore, this Special Issue will be devoted to new work on Numerical Linear Algebra and its applications. You are invited to share your state-of-the-art research results, present your application experiences, exchange new ideas and discuss future developments in Numerical Linear Algebra.

The topics of interest include but are not limited to the following:

  1. The application of differential geometry and topology in Numerical Linear Algebra;
  2. The perturbation analysis of eigensystem decompositions and matrix equations;
  3. Error analysis in matrix computations;
  4. The regularization of ill-posed problems;
  5. The numerical solution of linear systems and least squares problems;
  6. The numerical solution of eigenvalue problems;
  7. Large-scale problems;
  8. The Krylov subspace, Rayleigh–Ritz, Arnoldi and Lanczos methods;
  9. Computing the functions of matrices;
  10. Numerical matrix methods for solving ordinary and partial differential equations;
  11. Nonlinear eigenvalue methods;
  12. Software for matrix computations.

Prof. Dr. Petko Petkov
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • numerical linear algebra
  • matrix computations
  • perturbation analysis
  • least squares problems
  • eigenvalue problems
  • ill-posed problems
  • regularization methods
  • software for numerical matrix computations

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Published Papers (1 paper)

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Review

87 pages, 61280 KB  
Review
Differential Topology and Matrix Analysis: An Overview
by Petko H. Petkov
Axioms 2026, 15(3), 224; https://doi.org/10.3390/axioms15030224 - 16 Mar 2026
Viewed by 637
Abstract
This overview illustrates the application of methods from differential topology to several important problems in matrix analysis. In particular, it focuses on the use of smooth manifolds and smooth mappings to study fundamental issues such as the determination of matrix rank and the [...] Read more.
This overview illustrates the application of methods from differential topology to several important problems in matrix analysis. In particular, it focuses on the use of smooth manifolds and smooth mappings to study fundamental issues such as the determination of matrix rank and the computation of the Jordan form in the presence of uncertainties. Various aspects of numerical matrix analysis are discussed, including the genericity of matrix problems, characterization of singular sets in the parameter space, the distance to ill-posedness and its relation to problem conditioning. The conditioning of matrix problems is considered in both deterministic and probabilistic settings. The paper also addresses the regularization of ill-posed matrix problems in the presence of errors. Several examples are provided to illustrate these concepts and their practical relevance. The overview is intended for specialists from different fields who use matrix analysis in their work and do not have a strong background in differential topology. Full article
(This article belongs to the Special Issue New Advances in Numerical Linear Algebra and Its Applications)
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