阻尼最小二乘法.doc

阻尼最小二乘法
the Levenberg–Marquardt algorithm (LMA)[1]provides a numerical solution to the problem of minimizing a function, generally nonlinear, over a space of parameters of the function. These minimization problems arise especially in least squares curve fitting and nonlinear programming.
The LMA interpolates between the Gauss–Newton algorithm (GNA就是最小二乘) and the method of gradient LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be a bit slower than the GNA. LMA can also be viewed as Gauss–Newton using a trust region approach.
However, the LMA finds only a local minimum, not a global 。这是所有线性反演的通病。
The problem
The primary application of the Levenberg–Marquardt algorithm is in the least squares curve fitting problem: given a set of m empirical datum pairs ofindependent and dependent variables, (xi, yi), optimize the parameters β of the model curve f(x,β) so that the sum of the squares of the deviations
es minimal.
The solution
Like other numeric minimization algorithms, the Levenberg–Marquardt
algorithm is an iterative procedure. To start a minimization, the user has to provide an initial guess for the parameter vector, β. In cases with only one minimum, an uninformed stan