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Том 41, № 4 (2017)
- Год: 2017
- Статей: 7
- URL: https://journals.rcsi.science/0278-6419/issue/view/10805
Article
Numerical solution of Sylvester matrix equations with normal coefficients
Аннотация
Algorithms of the Bartels–Stewart type for the numerical solution of Sylvester matrix equations of modest size are modified for the case where the linear operators associated with these equations are normal. The superiority of the modified algorithms over the original ones is illustrated by numerical results.
153-156
On the boundary-value problem for a mixed-type equation: Asymptotic analysis and an effective numerical algorithm
Аннотация
A singularly perturbed boundary-value problem for an equation of mixed ellipticparabolic type is considered. The first part of this work is devoted to an asymptotic study of the solution to the problem. Modification of the boundary function method for mixed-type equations with small parameters at the highest derivatives is used. The second part is devoted to creating a numerical method that considers the structure of the solution for small parameter values. The idea of an approximate factorization of an elliptic operator into the product of two parabolic operators is employed. An effective numerical algorithm based on an asymptotic representation of the solution is developed.
157-164
Account for the nonlocal effect in light scattering by plasmonic nanoparticles in the hybrid scheme of the discrete sources method
Аннотация
A three dimensional problem of plane wave diffraction on a plasmonic nanoparticle is considered, with account for the nonlocal effect. A solution is constructed on the basis of a modified computational scheme of the discrete sources method. A numerical study of the nonlocal effect influence on the scattering properties of spherical nanoparticles upon their deformation is conducted.
165-172
A numerical way of solving the inverse problem for the wave equation in a medium with local inhomogeneity
Аннотация
The inverse problem of determining the boundary of local inhomogeneity for measuring a field in a bounded receivers location domain in a three-dimensional medium is considered for the wave equation. The problem is reduced to a system of integral equations. An iteration approach to solving the inverse problem is proposed, and the results from numerical experiments are presented.
173-178
An efficient numerical method for a mathematical model of a transport of coagulating particles
Аннотация
A new computational algorithm based on a fast way of computing integral operators describing the coagulation process is proposed for a mathematical model of coagulating particles. Using this algorithm, the computational complexity of each timestep of an explicit difference scheme can be substantially reduced. For each step, the complexity of execution is reduced from O(NM2) arithmetic operations to O(NMRlnM), where N is the number of mesh points along the physical coordinates of particles, M is the number of mesh points in a grid corresponding to sizes of coagulating particles, and R is the rank of a matrix corresponding to the values of the function of a coagulation kernel at mesh points. Using this approach, computations can be greatly accelerated, provided that kernel rank R is small.
179-186
Minimax mean-square thresholding risk in models with non-Gaussian noise distribution
Аннотация
The problem of nonparametric estimation of a signal function from noisy observations by thresholding its wavelet coefficients is considered. The orders of mean-square risk and asymptotically optimal thresholds under general assumptions on the noise distribution are calculated.
187-192
Complexity of function systems over a finite field in the class of polarized polynomial forms
Аннотация
The Shannon complexity of a function system over a q-element finite field which contains m functions of n variables in the class of polarized polynomial forms is exactly evaluated: LqPPF (n,m) = qn for all n ≥ 1, m ≥ 2, and all possible odd q. It has previously been known that L2PPF (n,m) = 2n and L3PPF (n,m) = 3n for all n ≥ 1 and m ≥ 2.
193-198