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A Hybrid Algorithm for Solving Nonlinear Least Squares Problems

Author: MengFanXue
Tutor: FanJinYan
School: Shanghai Jiaotong University
Course: Computational Mathematics
Keywords: Nonlinear least squares problems Nonlinear equations Gauss-Newton method Levenberg-Marquardt method Trust Region skills
CLC: O241.5
Type: Master's thesis
Year: 2011
Downloads: 308
Quote: 2
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Abstract


Nonlinear least squares problems is an important branch of the optimization problem , there are a lot of wide range of applications in the field of chemistry , spectroscopy, neural networks, robotics, signal analysis , medical and biological imaging . The first half of this article describes the common method for solving nonlinear least squares problem : Gauss - Newton method , the Levenberg - Marquardt method , quasi-Newton method and tensor methods . The second half is given a new algorithm based on Gauss-Newton method and trust region techniques . Such as F. OF LAMPARIELLO , given algorithm is based on iterative effect of the Gauss-Newton step , every several iterations of Gauss-Newton equation amendment to switch to the Levenberg-Marquardt step to do the iteration direction . Iterative step using the non-monotonic line search techniques , to ensure global convergence . Local superlinear convergence of the algorithm for zero residual problem . In this paper , on the basis of the above algorithm gives a hybrid algorithm based on Gauss-Newton method and the Levenberg-Marquardt method and trust region techniques modified Levenberg-Marquardt parameter , we prove that the new algorithm has global convergence , and for zero residual The amount of local quadratic convergence . Numerical experiments show that the new algorithm is feasible and very effective for the rank-deficient .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Numerical approximation
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