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Mathematics
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Numerical Algorithms: Computer Aspects and Related Topics
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Numerical Algorithms: Computer Aspects and Related Topics

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

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 1799

Special Issue Editors

Dr. Beata Bylina

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Guest Editor
Faculty of Mathematics, Physics and Computer Science, Maria Curie-Sklodowska University, 20-031 Lublin, Poland
Interests: computer communications; communication networks; algorithms; parallel processing; matrix decomposition; sparse matrix–vector multiplication; linear algebra
Dr. Jarosław Bylina

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Guest Editor
Faculty of Mathematics, Physics and Computer Science, Maria Curie-Sklodowska University, 20-031 Lublin, Poland
Interests: distributed computing; parallel computing; applied mathematics; Markov chains; numerical algorithms
Dr. Ivan Lirkov

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Guest Editor
Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Interests: speed computing and parallel algorithms; computational linear algebra; numerical methods for partial differential equations
Special Issues, Collections and Topics in MDPI journals
Dr. Przemysław Stpiczyński

E-Mail Website
Guest Editor
Institute of Computer Science, Maria Curie-Sklodowska University, 20-033 Lublin, Poland
Interests: parallel numerical algorithms; scientific computing; parallel programming; distributed computing; computer architectures

Special Issue Information

Dear Colleagues,

We are very happy to announce that the 16th Workshop on Computer Aspects of Numerical Algorithms (CANA’23) will take place in Warsaw, Poland, during 17–20 September 2023 in conjunction with the 18th Conference on Computer Science and Intelligence Systems FedCSIS 2023 (https://fedcsis.org/), an annual international conference that has been organized jointly by the Polish Information Processing Society (PTI), IEEE Poland Section Computer Society Chapter and Department of Mathematics and Information Sciences, Warsaw University of Technology, in 2023.

With this conference in mind, we would like to invite authors to submit an extended version of their most successful papers to this Special Issue. However, we want to mention that the Special Issue is also open to submissions from authors who are interested in the topic even if they have not attended the workshop. Topics to be discussed at this conference include (but are not limited to) the following:

  • Parallel numerical algorithms
  • Novel data formats for dense and sparse matrices
  • Libraries for numerical computations
  • Numerical algorithms testing and benchmarking
  • Analysis of rounding errors of numerical algorithms
  • Languages, tools and environments for programming numerical algorithms
  • Numerical algorithms on coprocessors (GPU, Intel Xeon Phi, etc.)
  • Paradigms of programming numerical algorithms
  • Contemporary computer architectures
  • Heterogeneous numerical algorithms
  • Applications of numerical algorithms in science and technology

Dr. Beata Bylina
Dr. Jarosław Bylina
Dr. Ivan Lirkov
Dr. Przemysław Stpiczyński
Guest Editors

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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • mathematics computing
  • parallel algorithms
  • distributed computing
  • scalable computing
  • numerical algorithms
  • parallel and distributed programming
  • computational optimization
  • computer architectures

Published Papers (3 papers)

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Research

13 pages, 606 KiB  
Article
Accurate Computations with Block Checkerboard Pattern Matrices
by Jorge Delgado, Héctor Orera and J. M. Peña
Mathematics 2024, 12(6), 853; https://doi.org/10.3390/math12060853 - 14 Mar 2024
Viewed by 445
Abstract
In this work, block checkerboard sign pattern matrices are introduced and analyzed. They satisfy the generalized Perron–Frobenius theorem. We study the case related to total positive matrices in order to guarantee bidiagonal decompositions and some linear algebra computations with high relative accuracy. A [...] Read more.
In this work, block checkerboard sign pattern matrices are introduced and analyzed. They satisfy the generalized Perron–Frobenius theorem. We study the case related to total positive matrices in order to guarantee bidiagonal decompositions and some linear algebra computations with high relative accuracy. A result on intervals of checkerboard matrices is included. Some numerical examples illustrate the theoretical results. Full article
(This article belongs to the Special Issue Numerical Algorithms: Computer Aspects and Related Topics)
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13 pages, 251 KiB  
Article
Efficiency of Various Tiling Strategies for the Zuker Algorithm Optimization
by Piotr Blaszynski, Marek Palkowski, Wlodzimierz Bielecki and Maciej Poliwoda
Mathematics 2024, 12(5), 728; https://doi.org/10.3390/math12050728 - 29 Feb 2024
Viewed by 528
Abstract
This paper focuses on optimizing the Zuker RNA folding algorithm, a bioinformatics task with non-serial polyadic dynamic programming and non-uniform loop dependencies. The intricate dependence pattern is represented using affine formulas, enabling the automatic application of tiling strategies via the polyhedral method. Three [...] Read more.
This paper focuses on optimizing the Zuker RNA folding algorithm, a bioinformatics task with non-serial polyadic dynamic programming and non-uniform loop dependencies. The intricate dependence pattern is represented using affine formulas, enabling the automatic application of tiling strategies via the polyhedral method. Three source-to-source compilers—PLUTO, TRACO, and DAPT—are employed, utilizing techniques such as affine transformations, the transitive closure of dependence relation graphs, and space–time tiling to generate cache-efficient codes, respectively. A dedicated transpose code technique for non-serial polyadic dynamic programming codes is also examined. The study evaluates the performance of these optimized codes for speed-up and scalability on multi-core machines and explores energy efficiency using RAPL. The paper provides insights into related approaches and outlines future research directions within the context of bioinformatics algorithm optimization. Full article
(This article belongs to the Special Issue Numerical Algorithms: Computer Aspects and Related Topics)
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14 pages, 1089 KiB  
Article
Iteration-Based Temporal Subgridding Method for the Finite-Difference Time-Domain Algorithm
by Penglong Xu and Jinjie Liu
Mathematics 2024, 12(2), 302; https://doi.org/10.3390/math12020302 - 17 Jan 2024
Cited by 1 | Viewed by 530
Abstract
A novel temporal subgridding technique is proposed for the finite-difference time-domain (FDTD) method to solve two-dimensional Maxwell’s equations of electrodynamics in the TEz mode. Based on the subgridding FDTD algorithm with a separated spatial and temporal interface, our method focuses on [...] Read more.
A novel temporal subgridding technique is proposed for the finite-difference time-domain (FDTD) method to solve two-dimensional Maxwell’s equations of electrodynamics in the TEz mode. Based on the subgridding FDTD algorithm with a separated spatial and temporal interface, our method focuses on the temporal subgridding region, as it is the main source of late-time instability. Different from other subgridding algorithms that work on the interpolation between coarse and fine meshes, our method stabilizes the solution by using iterative updating equations on the temporal coarse–fine mesh interface. This new method presents an alternative approach aimed at improving the stability of the subgridding technique without modifying the interpolation formulas. We numerically study the stability of the proposed algorithm via eigenvalue tests and by performing long-term simulations. We employ a refinement ratio of 2:1 in our study. Our findings indicate the stability of the conventional temporal subgridding FDTD algorithm with a magnetic field (Hz) interpolation. However, when electric fields (Ex and Ey) are utilized in interpolation, late-time instability occurs. In contrast, the proposed iteration-based method with an electric field interpolation appears to be stable. We further employ our method as the forward problem solver in the Through-the-Wall Radar (TWR) imaging application. Full article
(This article belongs to the Special Issue Numerical Algorithms: Computer Aspects and Related Topics)
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