In this work, a recursive Levenberg-Marquardt (LM) learning algorithm in the complex domain is developed and applied to the learning of an adaptive control scheme composed by ComplexValued Recurrent Neural Networks (CVRNN). We simplified the derivation of the LM learning algorithm using a diagrammatic method to derive the adjoint CVRNN used to obtain the gradient terms. Furthermore, we apply th...

Abstract: In testing digital waveform recorders, an important part is to fit a sinusoidal model to recorded data, and calculate the parameters that result in the best fit. Methods are already standardized; however, they demand high computational power. In this article a new, quick and accurate sinefitting algorithm will be shown based on Levenberg-Marquardt (LM) method. The constraints of conve...

An investigation of the neural network convergence and prediction based on three optimization algorithms, namely, Levenberg-Marquardt, conjugate gradient, and delta rule, is described. Several simulated neural networks built using the above three algorithms indicated that the Levenberg-Marquardt optimizer implemented as a back-propagation neural network converged faster than the other two algor...

For solving nonsmooth systems of equations, the Levenberg-Marquardt method and its variants are of particular importance because of their locally fast convergent rates. Finitely manymaximum functions systems are very useful in the study of nonlinear complementarity problems, variational inequality problems, Karush-Kuhn-Tucker systems of nonlinear programming problems, and many problems in mecha...

Multidimensional scaling is a fundamental problem in data analysis and have a lot of applications. It’s goal is to look for an Euclidean graphic representation of a given set of data in a “low’ dimensional space (generally in IR or IR). This problem can be formulated as a nonlinear global optimization problem. To solve it, a Lenvenberg-Marquardt method is used upon different cost functions. Res...

RNNs have local feedback loops within the network which allows them to shop earlier accessible patterns. This network can be educated with gradient descent back propagation and optimization technique such as second-order methods; conjugate gradient, quasi-Newton, Levenberg-Marquardt have also been used for networks training [14, 15]. But still this algorithm is not definite to find the global m...

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg-Marquardt method for solving inverse modeling problems w...