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...

We present two algorithms that compute the Newton polytope of a polynomial f defining a hypersurface H in Cn using numerical computation. The first algorithm assumes that we may only compute values of f—this may occur if f is given as a straightline program, as a determinant, or as an oracle. The second algorithm assumes that H is represented numerically via a witness set. That is, it computes ...

Resistant training in radial basis function (RBF) networks is the topic of this paper. In this paper, one modification of Gauss-Newton training algorithm based on the theory of robust regression for dealing with outliers in the framework of function approximation, system identification and control is proposed. This modification combines the numerical robustness of a particular class of non-quad...

A fast Newton–Krylov algorithm is presented that solves the turbulent Navier–Stokes equations on unstructured 2-D grids. Themodel of Spalart andAllmaras provides the turbulent viscosity and is loosely coupled to themean-flow equations. It is often assumed that the turbulence model must be fully coupled to obtain the full benefit of an inexact Newton algorithm. We demonstrate that a loosely coup...

The paper is an introduction to the use of classical Newton–Puiseux procedure, oriented towards algorithmic description it. This procedure allows obtain polynomial approximations for parameterizations branches algebraic plane curve at a singular point. We look approach that can be easily grasped and almost self-contained. illustrate algorithm first in completely worked out example with point mu...

In this paper, an interior point algorithm for linear programs is adapted for solving multistage stochastic linear programs. The algorithm is based on Monteiro and Adler’s path-following algorithm for deterministic linear programs. In practice, the complexity of the algorithm is linear with respect to the size of the sample space. The algorithm starts from a feasible solution of the problem and...