Related papers: Solving non-linear integral equations for laser pu…
In this article we propose a novel nonstationary iterated Tikhonov (NIT) type method for obtaining stable approximate solutions to ill-posed operator equations modeled by linear operators acting between Hilbert spaces. Geometrical…
Frequency-resolved optical gating (FROG) is probably the most popular technique for complete characterization of ultrashort laser pulses. In FROG, a reconstruction algorithm retrieves the pulse from a measured spectrogram, yet current FROG…
In this work, we suggest an easy-to-code higher-order finite volume semi-discrete scheme to analyze the nonlinear behavior of the electron-plasma oscillations by solving electron fluid equations numerically. The present method employs a…
We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations.…
This paper present a numerical method for solving nonlinear Fredholm integral equations. The method is based upon Newton type approximations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
We present a recursive algorithm for multi-coefficient inversion in nonlinear Helmholtz equations with polynomial-type nonlinearities, utilizing the linearized Dirichlet-to-Neumann map as measurement data. To achieve effective recursive…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
In inverse problems we aim to reconstruct some underlying signal of interest from potentially corrupted and often ill-posed measurements. Classical optimization-based techniques proceed by optimizing a data consistency metric together with…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer…
Newton's method has been an important approach for solving variational inequalities, quasi-Newton method is a good alternative choice to save computational cost. In this paper, we propose a new method for solving monotone variational…
Based on phase retrieval, lensless coherent imaging and in particular holography offers quantitative phase and amplitude images. This is of particular importance for spectral ranges where suitable lenses are challenging, such as for hard…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…
In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We…
In this article, we introduce a novel parallel-in-time solver for nonlinear ordinary differential equations (ODEs). We state the numerical solution of an ODE as a root-finding problem that we solve using Newton's method. The affine…
Regularization is necessary for solving nonlinear ill-posed inverse problems arising in different fields of geosciences. The base of a suitable regularization is the prior expressed by the regularizer, which can be non-adaptive or adaptive…
The laser flash method is highly regarded due to its applicability to a wide temperature range, from cryogenic temperatures to the melting point of refractory metals, and to extreme environments involving radioactive or hazardous materials.…