


Volume 65, Nº 7 (2025)
K 70-letiyu E.E. Tyrtyshnikova



General numerical methods
Eigenvalues of non-Hermitian banded Toeplitz matrices approaching simple points of the limiting set
Resumo
For large non-Hermitian banded Toeplitz matrices, it is well known that their eigenvalues cluster along a limiting set, which is formed by a finite union of closed analytic arcs. We consider general non-Hermitian banded Toeplitz matrices and extend the simple-loop method to obtain individual asymptotic expansions for eigenvalues approaching simple and non-degenerate points of the limiting set as the matrix order increases to infinity. We also develop an algorithm to effectively compute these expansions.



Tensor cross interpolation for global discrete optimization with application to Bayesian network inference
Resumo
Global discrete optimization is notoriously difficult due to the lack of gradient information and the curse of dimensionality, making exhaustive search infeasible. Tensor cross approximation is an efficient technique to approximate multivariate tensors (and discretized functions) by tensor product decompositions based on a small number of tensor elements, evaluated on adaptively selected fibers of the tensor, that intersect on submatrices of (nearly) maximum volume. The submatrices of maximum volume are empirically known to contain large elements, hence the entries selected for cross interpolation can also be good candidates for the globally maximal element within the tensor. In this paper we consider evolution of epidemics on networks, and infer the contact network from observations of network nodal states over time. By numerical experiments we demonstrate that the contact network can be inferred accurately by finding the global maximum of the likelihood using tensor cross interpolation. The proposed tensor product approach is flexible and can be applied to global discrete optimization for other problems, e.g. discrete hyperparameter tuning.



A FAST NUMERICAL METHOD FOR THE SOURCE RECONSTRUCTION IN THE COAGULATION-FRAGMENTATION EQUATION
Resumo



SYMMETRIC TRIANGULAR DECOMPOSITION FOR CONSTRUCTING APPROXIMATIONS TO SOLVING THE QUADRATIC ASSIGNMENT PROBLEM
Resumo



ADAPTIVE BLOCK ALGEBRAIC MULTIGRID METHOD FOR MULTIPHYSICS PROBLEMS
Resumo



K-OPTIMAL PRECONDITIONERS BASED ON APPROXIMATIONS OF INVERSE MATRICES
Resumo



ADAPTIVE PRIMAL–DUAL METHODS WITH AN INEXACT ORACLE FOR RELATIVELY SMOOTH OPTIMIZATION PROBLEMS AND THEIR APPLICATIONS TO RECOVERING LOW-RANK MATRICES
Resumo



APPLICATION OF THE MOSAIC-SKELETON MATRIX APPROXIMATION METHOD IN ELECTROMAGNETIC SCATTERING PROBLEMS
Resumo



BLOCK GENERALIZED METHOD OF MINIMAL INCONSISTENCIES
Resumo



Ordinary differential equations
RATIONAL COEFFICIENTS OF ORTHOGONAL DECOMPOSITIONS OF CERTAIN FUNCTIONS
Resumo



SOLVABILITY AND PROPERTIES OF CRITICAL POINTS OF LINEAR VOLTERRA INTEGRO-ALGEBRAIC EQUATIONS
Resumo






Partial Differential Equations
APPLICATION OF QUADRATURE FORMULAS FOR THE SIMPLE LAYER POTENTIAL TO THE EXTERNAL NEUMANN PROBLEM
Resumo



ON VARIATIONAL SETTINGS OF THE INVERSE COEFFICIENT PROBLEMS IN MAGNETIC HYDRODYNAMICS
Resumo



Mathematical physics
STUDY OF RESONANCE PROPERTIES OF PAIRED NANOPARTICLES WITH MESOSCOPIC BOUNDARY CONDITIONS BY THE DISCRETE SOURCE METHOD
Resumo



ON THE AMPLIFICATION OF THE GAS SUSPENSION MODEL WITH A GENERAL PRESSURE
Resumo


