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Ускорение итерационных методов решения линейных обратных задач на основе малорангового приближения
Журнал вычислительной математики и математической физики. 2026. Т. 66. № 1. С. 6–18.
Валиахметов Б. И., Лукьяненко Д. В., Тыртышников Е. Е.
In press
An efficient method is proposed for constructing a preconditioner for accelerated solution of systems of linear algebraic equations arising in solving linear inverse problems. The method relies on the properties of a low-rank approximation of the original system matrix and allows for a significant reduction in the number of iterations in iterative solution methods. Significant savings in computational resources can be achieved in the inverse problem of processing experimental data measured in a spatial domain separated from the domain of localization of the quantities to be reconstructed.
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Netherlands: ScienceDirect, 2025.
No ...
Added: June 28, 2026
Seidel A., Weske M., Montali M. et al., Information Systems 2026 Vol. 141 Article 102728
Business process management employs process models and event logs to represent the behavior of the information systems under study. Traditional case-centric notions consider the order of activities and events in isolated process instances. The emerging field of object-centric processes challenges this assumption by putting objects in the center. Object-centric process mining and modeling approaches identify ...
Added: June 27, 2026
IEEE, 2024.
A.S. Popov Russian Science and Technical Society with support from V. A. Trapeznikov Institute of Control Sciences, V.A. Kotelnikov Institute of Radio Engineering and Electronics, Autex Ltd. is leading the ХХVIII International Conference «Digital Signal Processing and its Applications — DSPA-2024» ...
Added: June 27, 2026
Ivchenko A., Дворкович А. В., Телекоммуникации 2020 Т. 12 С. 2–11
Dynamic Adaptive Streaming over HTTP (DASH) technology powers most multimedia services. Its specific features (re-buffering, quality switching, etc.) necessitate the development of specialized methods for assessing user subjective quality of experience (QoE) based on objective parameters. This article examines the impact of various metrics on QoE and presents assessment models with Spearman correlation coefficients up ...
Added: June 27, 2026
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2026 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Шестопёров А. И., Фомина Е. В., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Компьютерные исследования и моделирование 2022 Т. 14 № 6 С. 1255–1268
This work contains a description of the results of modeling the process of maintaining the readiness of a section of the road network under strikes of with specified parameters. A one-dimensional section of road up to 40 km long with a total number of strikes up to 100 during the work of the brigade is ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
Added: June 26, 2026
Stanislav Morozov, Calcolo 2026 Vol. 63 No. 2 Article 23
The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...
Added: May 22, 2026
Low-rank matrix and tensor approximations for compression of machine-learning interatomic potentials
Vorotnikov I., Romashov F., Rybin N. et al., Journal of Chemical Physics 2025 Vol. 163 No. 24 Article 244112
Machine-learning interatomic potentials (MLIPs) have become a mainstay in computationally guided materials science, surpassing traditional force fields due to their flexible functional form and superior accuracy in reproducing physical properties of materials. This flexibility is achieved through mathematically rigorous basis sets that describe interatomic interactions within a local atomic environment. The number of parameters in ...
Added: January 4, 2026
Kazeev V., Oseledets I., Maxim V. Rakhuba et al., Multiscale Modeling and Simulation 2022 Vol. 20 No. 3 P. 893–935
Homogenization in terms of multiscale limits transforms a multiscale problem with 𝑛+1n+1 asymptotically separated microscales posed on a physical domain 𝐷⊂ℝ𝑑D⊂Rd into a one-scale problem posed on a product domain of dimension (𝑛+1)𝑑(n+1)d by introducing 𝑛n so-called fast variables. This procedure allows one to convert 𝑛+1n+1 scales in 𝑑d physical dimensions into a single-scale structure in (𝑛+1)𝑑(n+1)ddimensions. We prove here that both the original, physical multiscale problem and ...
Added: October 30, 2022
Marcati C., Rakhuba M., Schwab C., Advances in Computational Mathematics 2022 Vol. 48 No. 3 Article 18
We analyze rates of approximation by quantized, tensor-structured representations of functions with isolated point singularities in ℝ3. We consider functions in countably normed Sobolev spaces with radial weights and analytic- or Gevrey-type control of weighted semi-norms. Several classes of boundary value and eigenvalue problems from science and engineering are discussed whose solutions belong to the ...
Added: October 30, 2022
Rakhuba M., SIAM Journal of Scientific Computing 2021 Vol. 43 No. 2 P. A800–A827
The aim of this paper is to propose a robust numerical solver, which is capable of efficiently solving a three-dimensional elliptic problem in a data-sparse quantized tensor format. In particular, we use the combined Tucker and quantized tensor train format (TQTT), which allows us to use astronomically large grid sizes. However, due to the ill-conditioning of discretized ...
Added: February 4, 2021
Rakhuba M., / Series math "Seminar for Applied Mathematics reports". 2019. No. 30.
The aim of this paper is to propose a robust numerical solver, which is capable of efficiently solving a three-dimensional elliptic problem in a data-sparse quantized tensor format. In particular, we use the combined Tucker and quantized tensor train format (TQTT), which allows us to use astronomically large grid sizes. However, due to ill-conditioning of discretized differential ...
Added: October 20, 2020
Oseledets I., Rakhuba M., André U., SIAM Journal on Numerical Analysis 2018 Vol. 56 No. 6 P. 3459–3479
In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimization on moving subspaces yields insightful reformulations of some known convergence conditions that focus on the interplay between the contractivity of classical multiplicative Schwarz methods with overlapping subspaces and ...
Added: October 20, 2020
Rakhuba M., Oseledets I., SIAM Journal of Scientific Computing 2018 Vol. 40 No. 2 P. A1149–A1170
In this work we generalize the Jacobi--Davidson method to the case when the eigenvector can be reshaped into a low-rank matrix. In this setting the proposed method inherits the advantages of the original Jacobi--Davidson method, has lower complexity, and requires less storage. We also introduce a low-rank version of the Rayleigh quotient iteration which naturally ...
Added: October 20, 2020