Levenberg | 您所在的位置:网站首页 › origin怎么用Levenberg-Marquardt › Levenberg |
Levenberg-Marquardt Method
Levenberg-Marquardt is a popular alternative to the Gauss-Newton method of finding the minimum of a function that is a sum of squares of nonlinear functions, Let the Jacobian of be denoted , then the Levenberg-Marquardt method searches in the direction given by the solution to the equations where are nonnegative scalars and is the identity matrix. The method has the nice property that, for some scalar related to , the vector is the solution of the constrained subproblem of minimizing subject to (Gill et al. 1981, p. 136). The method is used by the command FindMinimum[f, x, x0] when given the Method -> LevenbergMarquardt option. See alsoMinimum, Optimization Explore with Wolfram|AlphaMore things to try: optimization arrow's paradox 21.80144366645 ReferencesBates, D. M. and Watts, D. G. Nonlinear Regression and Its Applications. New York: Wiley, 1988.Gill, P. R.; Murray, W.; and Wright, M. H. "The Levenberg-Marquardt Method." §4.7.3 in Practical Optimization. London: Academic Press, pp. 136-137, 1981.Levenberg, K. "A Method for the Solution of Certain Problems in Least Squares." Quart. Appl. Math. 2, 164-168, 1944.Marquardt, D. "An Algorithm for Least-Squares Estimation of Nonlinear Parameters." SIAM J. Appl. Math. 11, 431-441, 1963.Referenced on Wolfram|AlphaLevenberg-Marquardt Method Cite this as:Weisstein, Eric W. "Levenberg-Marquardt Method." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Levenberg-MarquardtMethod.html Subject classifications |
CopyRight 2018-2019 实验室设备网 版权所有 |