In this paper, the problem of nonnegative matrix factorization (NMF) is considered. It is formulated as the optimization of a criterion with bound constraints. We propose an approach based on Givens parameterization of some positive vector, and criterion minimization is achieved using Levenberg-Marquardt algorithm. The performance of the developed NMF method is illustrated for the separation of...

A new, to my knowledge, procedure for retrieving the wave aberration from the point-spread function is presented. It uses the Levenberg-Marquardt optimization algorithm in a mutiresolution pyramidal scheme. The method, tested with simulated large aberrations without initial estimates, accelerates convergence and avoids stagnation in local minima.

Increasing electricity demand in Java-Madura-Bali, Indonesia, must be addressed appropriately to avoid blackout by determining accurate peak load forecasting. Econometric approach may not be sufficient to handle this problem due to limitation in modelling nonlinear interaction of factors involved. To overcome this problem, Elman and Jordan Recurrent Neural Network based on Levenberg-Marquardt l...

The aim of this paper is to propose a new Kalman Filter Recurrent Neural Network (KFRNN) topology and a recursive Levenberg-Marquardt (L-M) algorithm of its learning capable to estimate states and parameters of a highly nonlinear Continuous Stirred Tank Bioreactor (CSTR) in noisy environment. The estimated parameters and states obtained by the proposed KFRNN identifier are used to design an ind...

In this paper, we adopt the Levenberg-Marquardt (LM) algorithm to implement the nonlinear multivariable optimization for azimuth/elevation angle-of-arrival (AOA) estimation based on the Capon beamforming algorithm. The formulation is based on the fact that the cost function of the Capon algorithm can be expressed in a least-squares form. The performance in terms of the root mean square error (R...

This paper proposes a new Levenberg-Marquardt algorithm that is accelerated by adjusting a Jacobian matrix and a quasi-Hessian matrix. The proposed method partitions the Jacobian matrix into block matrices and employs the inverse of a partitioned matrix to find the inverse of the quasi-Hessian matrix. Our method can avoid expensive operations and save memory in calculating the inverse of the qu...

In this paper, we propose the block-diagonal matrix to approximate the Hessian matrix in the Levenberg Mar-quardt method in the training of neural networks. Two weight updating strategies, namely asynchronous and synchronous updating methods were investigated. Asyn-chronous method updates weights of one block at a time while synchronous method updates all weights at the same time. Variations of...

The rst part of this paper studies a Levenberg-Marquardt scheme for nonlinear inverse problems where the corresponding Lagrange (or regularization) parameter is chosen from an inexact Newton strategy. While the convergence analysis of standard implementations based on trust region strategies always requires the invertibility of the Fr echet derivative of the nonlinear operator at the exact solu...