In this paper, we present an inexact full Newton optimization method for the full waveform inversion algorithm in the frequency domain which utilizes simultaneous sources based upon the phase encoding technique. Tests show that the full Newton minimization method achieves a high convergence rate and a reasonably accurate reconstruction of the model parameters. Taking advantage of a direct solve...

Many algorithms have been proposed for finding a local minimum of a function f ( x ) f rom R" into R ~ using only function and gradient values. These include discrete Newton methods, quasi -Newton methods, and the conjugate gradient algorithm. For a discussion of these methods, see, for example [1]. There are classes of problems for which each of these methods is the most efficient. In this pap...

In this thesis I present a new algorithm OPT for matrix inversion that builds on a matrix multiplication subroutine. It is combined of Strassen’s matrix inversion algorithm and Newton approximation. OPT overcomes the linear lower bound in parallel runtime of Strassen’s inversion algorithm and traditional Gaussian elimination without the log-factor more work of Newton approximation. In particula...

We exhibit an algorithm which computes an approximation of the positive solutions of a family of boundary value problems with Neumann boundary conditions. Such solutions arise as the stationary solutions of a family of semilinear parabolic equations with Neumann boundary conditions. The algorithm is based on a nite dimensional Newton iteration associated with a suitable discretized version of t...

We introduce a well-developed Newton iterative (truncated Newton) algorithm for solving large-scale nonlinear systems. The framework is an inexact Newton method globalized by backtracking. Trial steps are obtained using one of several Krylov subspace methods. The algorithm is implemented in a Fortran solver called NITSOL that is robust yet easy to use and provides a number of useful options and...