本文介绍了Levenberg-Marquardt方法的原理和应用，以及如何用pyROOT编写相关的程序。Levenberg-Marquardt方法是一种非线性最小二乘拟合方法，可以用于物理模型与参数拟合中的优化问题。

The Levenberg-Marquardt method is a regularization technique for the Newton method applied to nonlinear equations, possibly constrained, and possibly with singular or nonisolated solutions. The paper reviews the literature on the subject, and discusses various convergence frameworks and results for smooth and piecewise smooth equations.

非线性最小二乘问题与Levenberg-Marquardt算法详解 ... 所以通常会通过矩阵分解，如 QR 分解或者 Cholesky 分解等方法来求解线性方程组以获得更好的效率以及稳定性。 ... 的 Hessian 矩阵，其是一个实对称矩阵。为了简洁，在不影响理解的情况下，后面有时会省略部分

Levenberg-Marquardt方法是一种非线性最小化算法，用于解决非线性最小二乘问题。它是通过在高斯牛顿方法和梯度下降方法之间取得平衡来改进收敛性和稳定性的。 该方法基于一个迭代过程，在每次迭代中，它通过调整参数来最小化目标函数的残差平方和。

The Levenberg-Marquardt method is a regularization technique for solving nonlinear equations, possibly constrained, with singular or nonisolated solutions. This paper reviews the literature on the subject, from a unified perspective, and obtains some new results on smooth and piecewise smooth equations, inexact subproblems, and globalization techniques.

The Levenberg-Marquardt method is a regularization technique for the Newton method applied to nonlinear equations, possibly constrained, and possibly with singular or nonisolated solutions. The paper reviews the literature on the subject, and discusses various convergence frameworks and results for smooth and piecewise smooth equations.