Falaleev MV, Romanova OA, Sinitsyn AV, Dreglea AI, Leont'ev RY, Sidorov DN On the Occasion of the 80th Birthday of Professor N. A. Sidorov // BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS. Vol.32. 2020. P.134-143. DOI: 10.26516/1997-7670.2020.32.134 The paper presents a brief overview of the main areas of research and educational activities of the founder of the Irkutsk school on the theory of differential operator equations with the irreversible operator in the main part, the professor...
Теги: nonlinear analysis , plasma , vlasov-maxwell equation , bifurcation , regularization , lyapunov-schmidt method , partial-differential-equations , 1st kind , operatorSizikov V., Sidorov D. Discrete Spectrum Reconstruction Using Integral Approximation Algorithm // Applied Spectroscopy. Vol.71. No.7. 2017. P.1640-1651. DOI: 10.1177/0003702817694181 An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of linear-nonlinear equations (SLNE) with respect to intensities and frequencies...
Теги: inverse problem of spectroscopy , discrete spectrum , system of linear and nonlinear equations , integral equations , regularization , resolution enhancement , integral approximation algorithm , lines intens , least-squares problems , variable projection , infrared... based on the piecewise constant and piecewise linear approximation of the exact solution are proposed for linear solutions. The accuracy of proposed numerical methods is O(1/N) and O(1/N-2) respectively. A certain iterative numerical scheme enjoying the regularization properties is suggested. Furthermore, generalized numerical method for nonlinear equations is adduced. The midpoint quadrature rule in all the cases is employed. In conclusion several numerical examples are applied in order to demonstrate ...
Теги: volterra integral equations , discontinuous kernels , direct quadrature method , regularization , evolving dynamical systems , midpoint quadrature , model , systems... algebraic equations without shift meshes techniques employment. We also propose generalized quadrature method for solution of Abel equation using the singular integral. Relaxed errors bounds are derived. In order to improve the accuracy we use Tikhonov regularization method. We demonstrate the efficiency of proposed techniques on infrared tomography problem. Numerical experiments show that it makes sense to apply regularization in case of highly noisy (about 10%) sources only. That is due to the known ...
Теги: linear algebra , linear equations , numerical methods , tomography , abel equation , generalized quadrature , infrared tomography , quadrature , regularization , singular kernel , integral equations
