Numerical Algorithms: Methods and Applications

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

Deadline for manuscript submissions: 30 September 2026 | Viewed by 600

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Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
Interests: high-speed computing and parallel algorithms; computational linear algebra; numerical methods for partial differential equations
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Special Issue Information

Dear Colleagues,

This Special Issue aims to bring together recent advances in the development and analysis of numerical algorithms, with an emphasis on both methodological innovations and their practical applications across scientific and engineering disciplines. We welcome contributions that address computational challenges in modeling, simulation, and data-intensive problems, offering efficient, accurate, and scalable numerical solutions.

Topics to be discussed at this conference include (but are not limited to) the following:

  • Novel numerical methods for differential equations;
  • Parallel numerical algorithms;
  • Uncertainty quantification and stochastic numerical schemes;
  • Hierarchical, adaptive, domain decomposition, and local refinement methods;
  • Robust preconditioning algorithms;
  • Monte Carlo methods and algorithms;
  • Numerical linear algebra;
  • Multiscale and multiphysics problem;
  • Machine learning-enhanced numerical solvers;
  • 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. Ivan Lirkov
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-anonymized 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
  • numerical algorithms
  • parallel algorithms
  • distributed computing
  • scalable computing
  • computational optimization
  • numerical schemes
  • Monte Carlo methods and algorithms
  • numerical linear algebra
  • multiscale and multiphysics problem
  • machine learning-enhanced numerical solvers

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Published Papers (1 paper)

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Research

27 pages, 401 KB  
Article
Optimality Notions for Resolvent Monte Carlo
by Tsvetelin Kostadinov and Ivan T. Dimov
Mathematics 2026, 14(16), 2930; https://doi.org/10.3390/math14162930 - 13 Aug 2026
Viewed by 163
Abstract
Resolvent Monte Carlo estimates eigenvalues of large matrices by sampling Markov chains and reading the target value off a truncated resolvent quotient, trading exact arithmetic for a stochastic error that the almost-optimal sampling scheme is designed to suppress. This paper studies when that [...] Read more.
Resolvent Monte Carlo estimates eigenvalues of large matrices by sampling Markov chains and reading the target value off a truncated resolvent quotient, trading exact arithmetic for a stochastic error that the almost-optimal sampling scheme is designed to suppress. This paper studies when that error vanishes outright. An exact closed-form identity is derived for the variance of the moment estimators of a general, possibly signed matrix, and is used to isolate a hierarchy of zero-variance notions ranging from the most local, which constrains only the first draws, through the finite-truncation regime that a practical run can certify, to the global regime in which every moment estimator is deterministic. Determinism of the estimator is separated from correctness of the eigenvalue it reports, and the exact conditions under which each notion holds are exhibited, together with the examples that separate them. A single edgewise condition, termed the eigen-triple condition, forces the truncated quotient to equal the target eigenvalue in finite samples; the associated moment and quotient variances are second order in the maximal edge defect and vanish at the eigen-triple. A linear-time procedure certifies the condition. Full article
(This article belongs to the Special Issue Numerical Algorithms: Methods and Applications)
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