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Mathematics
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Computational Methods for Numerical Linear Algebra
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Computational Methods for Numerical Linear Algebra

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C: Mathematical Analysis".

Deadline for manuscript submissions: 31 May 2026 | Viewed by 1202

Special Issue Editor

Dr. Junjun Pan

E-Mail Website
Guest Editor
Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
Interests: numerical linear algebra; nonnegative matrix factorization; tensor decomposition; numerical optimization; data mining; machine learning

Special Issue Information

Dear Colleagues,

This Special Issue on Computational Methods for Numerical Linear Algebra aims to highlight the latest advancements and innovative techniques in the field. Numerical linear algebra is foundational to various scientific and engineering applications, and efficient computational methods are crucial for solving large-scale problems that arise in data analysis, machine learning, simulations, and other fields.

We invite contributions that explore new algorithms, theoretical developments, and practical implementations in numerical linear algebra. Topics of interest include, but are not limited to, iterative methods for solving linear systems, eigenvalue problems, singular value decomposition, matrix and tensor factorization techniques, parallel and distributed computing approaches, and quantum computing. We also welcome studies that address numerical stability, complexity analysis, and applications of these methods in real-world scenarios.

By fostering collaboration and knowledge exchange among researchers and practitioners, this Special Issue aims to advance the state-of-the-art computational methods for numerical linear algebra, providing a comprehensive resource for those seeking to enhance their understanding and application of these critical techniques. We encourage authors to submit original research papers that contribute to this evolving field.

Dr. Junjun Pan
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • eigenvalue problems
  • singular value decomposition
  • matrix/tensor factorization techniques
  • parallel and distributed computing approaches
  • quantum computing

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Published Papers (2 papers)

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Research

20 pages, 2503 KB  
Article
On Invertibility of Large Binary Matrices
by Ibrahim Mammadov, Pavel Loskot and Thomas Honold
Mathematics 2026, 14(2), 270; https://doi.org/10.3390/math14020270 - 10 Jan 2026
Viewed by 406
Abstract
Many data processing applications involve binary matrices for storing digital information. At present, there are limited results in the literature about algorithms for inverting large binary matrices. This paper contributes the following three results. First, the divide-and-conquer methods for efficiently inverting large matrices [...] Read more.
Many data processing applications involve binary matrices for storing digital information. At present, there are limited results in the literature about algorithms for inverting large binary matrices. This paper contributes the following three results. First, the divide-and-conquer methods for efficiently inverting large matrices over finite fields such as Strassen’s matrix inversion often fail on singular sub-blocks, even if the original matrix is non-singular. It is proposed to combine Strassen’s method with the PLU factorization at each recursive step in order to obtain robust pivoting, which correctly inverts all non-singular matrices over any finite field. The resulting algorithm is shown to maintain the sub-cubic time complexity. Second, although there are theoretical studies on how to systematically enumerate all invertible matrices over finite fields without redundancy, no practical algorithm has been reported in the literature that is easy to understand and also suitable for enumerating large matrices. The use of Bruhat decomposition has been proposed to enumerate all invertible matrices. It leverages the linear group-theoretic structure and defines an ordered sequence of invertible matrices, so that each matrix is generated exactly once. Third, large binary matrices have about 29% probability to be invertible. In some applications, it may be desirable to repair the singular matrices by performing a small number of bit-flips. It is shown that the minimum number of bit-flips is equal to the matrix rank deficiency, i.e., the minimum Hamming distance from the general linear group. The required bit-flips are identified by pivoting during the matrix inversion, so the matrix rank can be restored. The correctness and the time complexity of the proposed algorithms were verified both theoretically and empirically. The reference implementation of these algorithms in C++ is available on Github. Full article
(This article belongs to the Special Issue Computational Methods for Numerical Linear Algebra)
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19 pages, 744 KB  
Article
A Spectral Approach to Solve High-Order Ordinary Differential Equations: Improved Operational Matrices for Exponential Jacobi Functions
by Hany Mostafa Ahmed
Mathematics 2025, 13(19), 3154; https://doi.org/10.3390/math13193154 - 2 Oct 2025
Viewed by 558
Abstract
This paper presents a novel numerical approach to handling ordinary differential equations (ODEs) with initial conditions (ICs) by introducing generalized exponential Jacobi functions (GEJFs). These GFJFs satisfy the associated ICs. A crucial part of this approach is using the spectral collocation method (SCM) [...] Read more.
This paper presents a novel numerical approach to handling ordinary differential equations (ODEs) with initial conditions (ICs) by introducing generalized exponential Jacobi functions (GEJFs). These GFJFs satisfy the associated ICs. A crucial part of this approach is using the spectral collocation method (SCM) and building operational matrices (OMs) for the ordinary derivatives (ODs) of GEJFs. These lead to efficient and accurate computations. The suggested algorithm’s convergence and error analysis is proved. We present numerical examples to demonstrate the applicability of the approach. Full article
(This article belongs to the Special Issue Computational Methods for Numerical Linear Algebra)
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