The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets. The Gauss–Newton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the least-squares equation. The quasi-Newton method has also been used to reduce the computer time. In this...

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an...

The Gauss-Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well-suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an...

In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve class nonconvex optimization problems involving low-rank matrix variables. As opposed standard GN method, our algorithm allows one handle general smooth convex objective function. We show, under mild conditions, that proposed globally and locally converges stationary point original problem. also show empiric...

In this paper, we present the Gauss-Newton method as a unified approach to estimating noise parameters of the prevalent non-linear compensation models, such as vector Taylor series (VTS), data-driven parallel model combination (DPMC), and unscented transform (UT), for noise-robust speech recognition. While iterative estimation of noise means in a generalized EM framework has been widely known, ...

We introduce in the present paper a Gauss–Newton-type method for solving generalized equations defined by sums of differentiable mappings and set-valued mappings in Banach spaces. Semi-local convergence and local convergence of the Gauss–Newton-type method are analyzed.

This paper describes a fall-back procedure for use with the Gauss-Newton method for nonlinear least-squares problems. While the basic Gauss-Newton algorithm is often successful, it is well-known that it can sometimes generate poor search directions and exhibit slow convergence. For dealing with such situations we suggest a new two-dimensional search strategy. Numerical experiments indicate that...