On the Rate of Convergence of the Levenberg-Marquardt Method
On the Rate of Convergence of the Levenberg-Marquardt Method
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DOI：
10.1007/978-3-7091-6217-0_18
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
N. Yamashita;M. Fukushima
中科院分区：
文献类型：
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作者：
N. Yamashita;M. Fukushima
本文考虑求解非线性方程组F（x）= 0的Levenberg-Marquardt方法（LMM）的收敛速度，其中F是从Rn到Rm的映射.众所周知，当m = n，F的雅可比矩阵在解x处是非奇异的，并且初始点选择得足够接近x时，LMM具有二次收敛速度。在本文中，我们表明，如果
We consider a rate of convergence of the Levenberg-Marquardt method (LMM) for solving a system of nonlinear equations F(x) = 0, where F is a mapping from Rn into Rm. It is well-known that LMM has a quadratic rate of convergence when m = n, the Jacobian matrix of F is nonsingular at a solution x and an initial point is chosen sufficiently close to x. In this paper, we show that if