A Brief Description of the Levenberg-Marquardt Algorithm Implemened by levmar

Introduction

The Levenberg-Marquardt(LM) algorithm is an iterative technique that locates the minimum of a multivariate function that is expressed as the sum of squares of non-linear real-valued functions. It has become a standard technique for non-linear least-squares problems, widely adopted in a broad spectrum of disciplines. LM can be thought of as a combination of steepest descent and the Gauss-Newton method. When the current solution is far from the correct one, the algorithm behaves like a steepest descent method:slow, but guaranteed to converge. When the current solution is close to the correct solution, it becomes a Gauss-Newton method.

简介

买夸特算法是一种遍历算法，用于求解多元方程的非线性最小二乘解。它已经成为一种求最小二乘解的标准技术手段，应用范围很广。LM算法可以被认为是最大梯度法和高斯-牛顿法的综合。当当前的解离正确解很远时，它相当于最大梯度法：慢，但是一定能够收敛。当当前的解接近于正确解时，它又成为了高斯-牛顿法。