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Solvability and bifurcation of solutions of nonlinear equations with fredholm operator

Sidorov N., Sidorov D., Dreglea A. Solvability and bifurcation of solutions of nonlinear equations with fredholm operator // Symmetry. Vol.12. No.6. ID: 912. 2020. DOI: 10.3390/SYM12060912 The necessary and sufficient conditions of existence of the nonlinear operator equations' branches of solutions in the neighbourhood of branching points are derived. The approach is based on the reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis...

Теги: asymptotics , bifurcation points , branch points , fredholm operator , iterations , regularization , uniformization
Discrete Spectrum Reconstruction Using Integral Approximation Algorithm

Sizikov 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
Numeric solution of Volterra integral equations of the first kind with discontinuous kernels

... 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
Generalized quadrature for solving singular integral equations of Abel type in application to infrared tomography

... 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


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