In this paper, we propose a hybrid Gauss-Newton structured BFGS method with a new update formula and a new switch criterion for the iterative matrix to solve nonlinear least squares problems. We approximate the second term in the Hessian by a positive definite BFGS matrix. Under suitable conditions, global convergence of the proposed method with a backtracking line search is established. Moreov...

Classification of line-of-sight (LOS) or non-LOS (NLOS) propagation is critical for most pulsed ultrawideband localisation systems. In this letter, first, the authors propose a two-dimensional (2D) LOS/NLOS classification scheme that uses skewness of the channel impulse/pulse response, which has not been used by existing work. The log-likelihood ratio of the 2D LOS/NLOS classification is used t...

In this paper, a new adjustment to the damping parameter of the Levenberg-Marquardt algorithm is proposed to save training time and to reduce error oscillations. The damping parameter of the Levenberg-Marquardt algorithm switches between a gradient descent method and the Gauss-Newton method. It also affects training speed and induces error oscillations when a decay rate is fixed. Therefore, our...

We construct a fast method, OðN logNÞ, for the computation of discrete Gauss transforms with complex parameters, capable of dealing with unequally spaced grid points. The method is based on Fourier techniques, and in particular it makes use of a modified unequally spaced fast Fourier transform algorithm, in combination with previously suggested divide and conquer strategies for ordinary fast Ga...

We give an expression, in terms of the so-called Hermitian intrinsic volumes, for the measure of the set of complex r-planes intersecting a regular domain in any complex space form. Moreover, we obtain two different expressions for the Gauss-BonnetChern formula in complex space forms. One of them expresses the Gauss curvature integral in terms of the Euler characteristic and some Hermitian intr...

This paper presents the design and analysis of an adaptive algorithm for tracking the amplitude, phase and frequency of the fundamental, harmonics and interharmonics present in time-varying power sinusoid in white noise. If frequency, amplitude and phase of the multiple sinusoids become nonstationary, they are estimated as an unconstrained optimization problem using robust and low complexity mu...

Recently a novel approach to nonlinear function approximation using hinging hyperplanes, was reported by L. Breiman 3]. In this contribution we have combined smooth hinging hyperplanes and the eecient initializa-tion procedure existing for hinging hyperplanes in 3], with a Gauss-Newton procedure, see 4], to perform the nal adjustment of the smooth hinging hyperplanes. This combination uses the ...

This paper describes a method of dogleg trust-region steps, or restricted Levenberg-Marquardt steps, based on a projection process onto the Krylov subspaces for neural networks nonlinear least squares problems. In particular, the linear conjugate gradient (CG) method works as the inner iterative algorithm for solving the linearized Gauss-Newton normal equation, whereas the outer nonlinear algor...

Methods of interval arithmetic can be used to reliably find with certainty all solutions to nonlinear systems of equations. In such methods, the system is transformed into a linear interval system and a preconditioned interval Gauss-Seidel method may then be used to compute such solution bounds. In this work, a new heuristic for solving polynomial systems is presented, called reordering techniq...

In order to limit the computational cost of the variational data assimilation process, we study the application of the multigrid methods to solve this optimal control system. These methods are used to accelerate an iterative method by solving for the error on low resolution grids. We define two multigrid algorithms and its convergence properties. The first one is based on the Full Approximation...