排序方式: 共有35条查询结果,搜索用时 390 毫秒
1.
A new implementation of the Marquardt method for the nonlinear least-squares problem is presented. The algorithm is very simple but its performance with nine test functions is at least comparable with either Davidon-Fletcher-Powell's method or Moré's adaptive Marquardt method. 相似文献
2.
A modified Levenberg–Marquardt method for solving singular systems of nonlinear equations was proposed by Fan [J Comput Appl Math. 2003;21;625–636]. Using trust region techniques, the global and quadratic convergence of the method were proved. In this paper, to improve this method, we decide to introduce a new Levenberg–Marquardt parameter while also incorporate a new nonmonotone technique to this method. The global and quadratic convergence of the new method is proved under the local error bound condition. Numerical results show the new algorithm is efficient and promising. 相似文献
3.
Ali Namadchian Mehdi Ramezani 《Numerical Methods for Partial Differential Equations》2020,36(3):637-653
The Fokker–Planck equation is a useful tool to analyze the transient probability density function of the states of a stochastic differential equation. In this paper, a multilayer perceptron neural network is utilized to approximate the solution of the Fokker–Planck equation. To use unconstrained optimization in neural network training, a special form of the trial solution is considered to satisfy the initial and boundary conditions. The weights of the neural network are calculated by Levenberg–Marquardt training algorithm with Bayesian regularization. Three practical examples demonstrate the efficiency of the proposed method. 相似文献
4.
5.
6.
Naveed Ahmad Khan Fahad Sameer Alshammari Carlos Andrs Tavera Romero Muhammad Sulaiman 《Entropy (Basel, Switzerland)》2021,23(12)
In this paper, we have analyzed the mathematical model of various nonlinear oscillators arising in different fields of engineering. Further, approximate solutions for different variations in oscillators are studied by using feedforward neural networks (NNs) based on the backpropagated Levenberg–Marquardt algorithm (BLMA). A data set for different problem scenarios for the supervised learning of BLMA has been generated by the Runge–Kutta method of order 4 (RK-4) with the “NDSolve” package in Mathematica. The worth of the approximate solution by NN-BLMA is attained by employing the processing of testing, training, and validation of the reference data set. For each model, convergence analysis, error histograms, regression analysis, and curve fitting are considered to study the robustness and accuracy of the design scheme. 相似文献
7.
Naveed Ahmad Khan Fahad Sameer Alshammari Carlos Andrs Tavera Romero Muhammad Sulaiman Ghaylen Laouini 《Molecules (Basel, Switzerland)》2021,26(23)
In this study, we have investigated the mathematical model of an immobilized enzyme system that follows the Michaelis–Menten (MM) kinetics for a micro-disk biosensor. The film reaction model under steady state conditions is transformed into a couple differential equations which are based on dimensionless concentration of hydrogen peroxide with enzyme reaction and substrate within the biosensor. The model is based on a reaction–diffusion equation which contains highly non-linear terms related to MM kinetics of the enzymatic reaction. Further, to calculate the effect of variations in parameters on the dimensionless concentration of substrate and hydrogen peroxide, we have strengthened the computational ability of neural network (NN) architecture by using a backpropagated Levenberg–Marquardt training (LMT) algorithm. NNs–LMT algorithm is a supervised machine learning for which the initial data set is generated by using MATLAB built in function known as “pdex4”. Furthermore, the data set is validated by the processing of the NNs–LMT algorithm to find the approximate solutions for different scenarios and cases of mathematical model of micro-disk biosensors. Absolute errors, curve fitting, error histograms, regression and complexity analysis further validate the accuracy and robustness of the technique. 相似文献
8.
《Applied Mathematical Modelling》2003,27(12):1035-1049
This article describes theoretical and experimental results on phase reflection diffraction gratings. Based on Fourier optics the mathematical formulation describing diffraction dispersion of light from a relief grating of the trapezium profile is derived. We propose a method that lets us estimate the grating’s geometric parameters in a versatile modelling system. We have designed an original programme that estimates diffraction intensities and calculates diffraction efficiency. The estimated intensities are used to reconstruct the grating’s geometrical properties using our mathematical model. The precision of the method is evaluated as the deviation of obtained results from microscopy data. 相似文献
9.
Juliano B. Francisco José Mario Martínez Leandro Martínez 《Journal of mathematical chemistry》2006,40(4):349-377
A theory of globally convergent trust-region methods for self-consistent field electronic structure calculations that use the density matrices as variables is developed. The optimization is performed by means of sequential global minimizations of a quadratic model of the true energy. The global minimization of this quadratic model, subject to the idempotency of the density matrix and the rank constraint, coincides with the fixed-point iteration. We prove that the global minimization of this quadratic model subject to the restrictions and smaller trust regions corresponds to the solution of level-shifted equations. The precise implementation of algorithms leading to global convergence is stated and a proof of global convergence is provided. Numerical experiments confirm theoretical predictions and practical convergence is obtained for difficult cases, even if their geometries are highly distorted. The reduction of the trust region is performed by a strategy that uses the structure of the energy function providing the algorithm with a nice practical behavior. This framework may be applied to any problem with idempotency constraints and for which the derivative of the objective function is a symmetric matrix. Therefore, application to calculations based both on Hartree–Fock or Kohn–Sham density functional theory are straightforward. 相似文献
10.
We extend the theory of Sobolev gradients to include variable metric methods, such as Newton’s method and the Levenberg–Marquardt method, as gradient descent iterations associated with stepwise variable inner products. In particular, we obtain existence, uniqueness, and asymptotic convergence results for a gradient flow based on a variable inner product. 相似文献