A Numerical Method for Inverse Spectral Problems

Кадченко, С.И.; Zakirova, G. A.

doi:10.14529/mmp150307

Cited by 13 publications

(3 citation statements)

References 2 publications

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“…Numerous eigenvalue calculations n µ ɶ of boundary problems generated by discrete semi-bounded from below operators for 50 n ≤ calculated by formulas (3) and the Galerkin method are in good agreement [1].…”

Section: Introductionmentioning

confidence: 76%

“…is the Galerkin approximation of order n to the corresponding eigenvalues k µ of the operator L. Formulas (3) allow, as shown in [1], to calculate the approximate eigenvalues of discrete semibounded operators with high computational efficiency. Unlike classical methods, they drastically reduce the amount of computation, solve the problem of finding the eigenvalues of any matrices of high order.…”

Section: Introductionmentioning

confidence: 99%

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Calculation of Discrete Semi-Bounded Operators’ Eigenvalues With Large Numbers

Кадченко¹,

Zakirova²,

Ryazanova³

et al. 2019

MMPh

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In previous works of the article's authors on development of the Galerkin method, linear formulas for calculating the approximate eigenvalues of discrete lower semi-bounded operators have been obtained. The formulas allow calculating the eigenvalues of the specified operators of any number, regardless of whether the eigenvalues of the previous numbers are known or not. At that, it is possible to calculate the eigenvalues with large numbers when application of the Galerkin method is becoming difficult. It is shown that eigenvalues of small numbers of various boundary-value problems, generated by discrete lower semibounded operators and calculated by linear formulas and by the Galerkin method, are in a good conformity.In this paper we use linear formulas to calculate approximate eigenvalues with large numbers of discrete lower semi-bounded operators. Results of calculation of eigenvalues by linear formulas and by known asymptotic formulas for two spectral problems are given. Comparison of the results of calculations of the approximate eigenvalues shows that they almost coincide for sufficiently large numbers. This proves the fact that linear formulas can be used for the considered spectral problems and sufficiently large numbers of eigenvalues.Keywords: spectral problem; discrete operators; semi-bounded operators; eigenvalues and eigenfunctions of an operator; Galerkin method. Kadchenko S.I., Zakirova G.A., Calculation of Discrete Semi-Bounded Operators' Ryazanova L.S., Torshina O.A. Eigenvalues with Large Numbers

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Section: Introductionmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Calculation of Discrete Semi-Bounded Operators’ Eigenvalues With Large Numbers

Кадченко¹,

Zakirova²,

Ryazanova³

et al. 2019

MMPh

Self Cite

View full text Add to dashboard Cite

show abstract

“…Theorem 6. For any α ∈ R, λ ∈ R + , η 0 ∈ U L L 2 , solution η = η(t) of problem (19), (20) has exponential dichotomies, and I + L L 2 and I − L L 2 of form (21), (22) are infinite-dimensional stable and finite-dimensional unstable invariant spaces of equation (19), respectively. Remark 1.…”

Section: Exponential Dichotomies Of the Barenblatt-zheltov-kochina Stmentioning

confidence: 99%

Exponential Dichotomies in Barenblatt-Zheltov-Kochina Model in Spaces of Differential Forms with "Noise''

Kitaeva¹,

Шафранов²,

Sviridyuk³

2019

Bulletin SUSU MMP

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We investigate stability of solutions in linear stochastic Sobolev type models with the relatively bounded operator in spaces of smooth differential forms defined on smooth compact oriented Riemannian manifolds without boundary. To this end, in the space of differential forms, we use the pseudo-differential Laplace-Beltrami operator instead of the usual Laplace operator. The Cauchy condition and the Showalter-Sidorov condition are used as the initial conditions. Since "white noise" of the model is non-differentiable in the usual sense, we use the derivative of stochastic process in the sense of Nelson-Gliklikh. In order to investigate stability of solutions, we establish existence of exponential dichotomies dividing the space of solutions into stable and unstable invariant subspaces. As an example, we use a stochastic version of the Barenblatt-Zheltov-Kochina equation in the space of differential forms defined on a smooth compact oriented Riemannian manifold without boundary.

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An approximate solution of inverse spectral problem for perturbed self-adjoint operator

Zakirova

2016

2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)

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A Numerical Method for Inverse Spectral Problems

Cited by 13 publications

References 2 publications

Calculation of Discrete Semi-Bounded Operators’ Eigenvalues With Large Numbers

Calculation of Discrete Semi-Bounded Operators’ Eigenvalues With Large Numbers

Exponential Dichotomies in Barenblatt-Zheltov-Kochina Model in Spaces of Differential Forms with "Noise''

An approximate solution of inverse spectral problem for perturbed self-adjoint operator

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