Full Waveform Inversion (FWI) is a powerful method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This method consists in minimizing a distance between predicted and recorded data. The predicted data is computed as the solution of a wave propagation problem. Conventional numerical methods for the resolution of FWI problems are gradient-based methods, ...

The theoretical foundation of path-following methods is the performance analysis (damped) Newton step on class self-concordant functions. However, bounds available in literature and used design are not optimal. In this contribution we use optimal control theory to compute length method functions, as a function initial decrement, resulting worst-case decrease decrement. exact expressed terms sol...

Given a C1 path of systems of homogeneous polynomial equations ft, t ∈ [a, b] and an approximation xa to a zero ζa of the initial system fa, we show how to adaptively choose the step size for a Newton based homotopy method so that we approximate the lifted path (ft, ζt) in the space of (problems, solutions) pairs. The total number of Newton iterations is bounded in terms of the length of the li...

The inexact primal-dual interior point method which is discussed in this paper chooses a new iterate along an approximation to the Newton direction. The method is the Kojima, Megiddo, and Mizuno globally convergent infeasible interior point algorithm The inexact variation is shown to have the same convergence properties accepting a residual in both the primal and dual Newton step equation also ...

In this paper, an iterative method was considered for solving the absolute value equation (AVE). We suggest a two-step in which well-known Gauss quadrature rule is corrector step and generalized Newton taken as predictor step. The convergence of proposed established under some acceptable conditions. Numerical examples prove consistency capability new method.

Full Waveform Inversion (FWI) is a promising seismic imaging method. It aims at computing quantitative estimates of the subsurface parameters (bulk wave velocity, shear wave velocity, rock density) from local measurements of the seismic wavefield. Based on a particular wave propagation engine for wavefield estimation, it consists in minimizing iteratively the distance between the predicted wave...