A batch training algorithm for feed-forward networks is proposed which uses Newton’s method to estimate a vector of optimal learning factors, one for each hidden unit. Backpropagation, using this learning factor vector, is used to modify the hidden unit’s input weights. Linear equations are then solved for the network’s output weights. Elements of the new method’s Gauss-Newton Hessian matrix ar...

A NEW multigrid relaxation scheme is developed for the steady-state solution of the Euler and Navier-Stokes equations. The lower-upper Symmetric-Gauss-Seidel method (LUSGS) does not require flux splitting for approximate Newton iteration. The present method, which is vectorizable and unconditionally stable, needs only scalar diagonal inversions. Application to transonic flow shows that the new ...

We propose a non-iterative solution to the PnP problem—the estimation of the pose of a calibrated camera from n 3D-to-2D point correspondences—whose computational complexity grows linearly with n. This is in contrast to state-of-the-art methods that are O(n) or even O(n), without being more accurate. Our method is applicable for all n ≥ 4 and handles properly both planar and non-planar configur...

Based on the perspective view of non-linear model fitting, a new algorithm for space resection based on Levenberg-Marquardt algorithm was developed in this paper. The relationship between the new algorithm and the current one, which is commonly implemented in the commercial software, was also discussed. The experimental evaluation of both algorithms with different level of inaccurate initial ap...

The local quadratic convergence of the Gauss-Newton method for convex composite optimization f = h ◦ F is established for any convex function h with the minima set C, extending Burke and Ferris’ results in the case when C is a set of weak sharp minima for h.

This paper shows a new approach for non-linear least squares fitting with NURBS as curves and surfaces to measured data by the Gauss-Newton method. A Trust Region algorithm is used to reach global convergence as well as variable substitution and simple bounds. Key–Words: Non-linear least squares, NURBS, curve and surface fitting, reverse engineering, optimisation, GaussNewton

We present a set of C++ classes that realize an abstract inexact Gauss Newton method in combination with a continuation process for the solution of parameter dependent nonlinear problems. The object oriented approach allows the continuation of diierent types of solutions within the same framework.

We introduce an inexact Gauss-Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties.

On the basis of new iterative technique designed by Zhongli Liu in 2016 with convergence orders three and five, an extension to order six can be found this paper. The study high-convergence-order methods under weak conditions is extreme importance, because higher means that fewer iterations are carried out achieve a predetermined error tolerance. In enhance practicality these Liu, analysis with...

The goal of this paper is to develop a general approach to solution of ill-posed nonlinear problems in a Hilbert space based on continuous processes with a regularization procedure. To avoid the ill-posed inversion of the Fréchet derivative operator a regularizing one-parametric family of operators is introduced. Under certain assumptions on the regularizing family a general convergence theorem...