We describe a generalized Levenberg-Marquardt method for computing critical points of the Ginzburg-Landau energy functional which models superconductivity. The algorithm is a blend of a Newton iteration with a Sobolev gradient descent method, and is equivalent to a trust-region method in which the trustregion radius is defined by a Sobolev metric. Numerical test results demonstrate the method t...

Efficient second order algorithm for training feedforward neural networks is presented. The algorithm has a similar convergence rate as the Lavenberg-Marquardt (LM) method and it is less computationally intensive and requires less memory. This is especially important for large neural networks where the LM algorithm becomes impractical. Algorithm was verified with several examples.

This paper presents an efficient method for updating the structural finite element model. Model updating is performed through minimizing the difference of recorded acceleration of real damaged structure and hypothetical damaged structure, by updating physical parameters in each phase using iterative process of Levenberg-Marquardt algorithm. This algorithm is based on sensitivity analysis and pr...

A novel algorithm is proposed for CANDECOMP/PARAFAC tensor decomposition to exploit best rank-1 tensor approximation. Different from the existing algorithms, our algorithm updates rank-1 tensors simultaneously in-parallel. In order to achieve this, we develop new all-at-once algorithms for best rank-1 tensor approximation based on the Levenberg-Marquardt method and the rotational update. We sho...

An advanced operational semi-empirical algorithm for processing satellite remote sensing data in the visible region is described. Based on the Levenberg-Marquardt multivariate optimization procedure, the algorithm is developed for retrieving major water colour producing agents: chlorophyll-a, suspended minerals and dissolved organics. Two assurance units incorporated by the algorithm are intend...

Incorporating higher-order optimization functions, such as Levenberg–Marquardt (LM) have revealed better generalizable solutions for deep learning problems. However, these functions suffer from very large processing time and training complexity especially datasets become large, in multi-view classification problems, where finding global optima is a costly problem. To solve this issue, we develo...

An approach is described to the numerical solution of order conditions for RungeKutta methods whose solutions evolve on a given manifold. This approach is based on least squares minimization using the Levenberg-Marquardt algorithm. Examples of methods of order four, ve and six are given and numerical experiments are presented which con rm that the derived methods have the expected order of accu...

In this study, the feedforward neural networks (FNNs) were applied for concentration estimation of formaldehyde. Contrasting with previous studies on binary gas mixtures, fourcomponent gas mixtures containing formaldehyde, ethanol, acetone and toluene were investigated in this paper. Experimental results showed that Levenberg-Marquardt algorithm was fast and efficient for quantitative analysis ...

In this paper, we propose an artificial neural network (ANN) as a design technique for multilayer circular microstrip antennas based on Levenberg Marquardt training algorithm for modelling, simulation and optimization. Levenberg – Marquart (LM) algorithm has been used to train the MultiLayer Perceptron Neural Networks (MLPNNs). In the design procedure, the feed forward network is defined as a s...

Background: Preterm births are babies that are born before 37 weeks of gestation. The premature delivery of babies is regarded as a major global public health issue with those affected at greater risk of developing short and long-term complications. The care provided for premature infants has significantly improved. However, it has had no impact on reducing the prevalence of preterm birth. Ther...