Adaptive Smoothing Method, Deterministically Computable Generalized Jacobians, and the Newton Method

2001 ◽  
Vol 109 (1) ◽  
pp. 215-224 ◽  
Author(s):  
H. Xu
Keyword(s):  
Newton Method ◽  
Smoothing Method ◽  
Adaptive Smoothing ◽  
Generalized Jacobians

scholarly journals Adaptive Smoothing Method For Computer Derivation of K-Indices

1991 ◽  
Vol 104 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Krzysztof Nowożyński ◽  
Tomasz Ernst ◽  
Jerzy Jankowski
Keyword(s):  
Smoothing Method ◽  
Adaptive Smoothing

A Smoothing Method for Solving the NCP Based on a New Smoothing Approximate Function

2013 ◽  
Vol 462-463 ◽  
pp. 294-297
Author(s):  
Wei Meng ◽  
Zhi Yuan Tian ◽  
Xin Lei Qu
Keyword(s):  
Global Convergence ◽  
Newton Method ◽  
Complementarity Problems ◽  
Numerical Results ◽  
Nonlinear Complementarity Problems ◽  
Smoothing Method ◽  
Smoothing Newton Method ◽  
Nonlinear Complementarity ◽  
Approximate Function

A new smoothing approximate function of the FischerBurmeister function is given. A modified smoothing Newton method based on the function is proposed for solving a kind of nonlinear complementarity problems. Under suitable conditions, the global convergence of the method is proved. Numerical results show the effectiveness of the method.

An Adaptive Smoothing Method for Continuous Minimax Problems

2015 ◽  
Vol 32 (01) ◽  
pp. 1540001
Author(s):  
Hongxia Yin
Keyword(s):  
Minimax Problems ◽  
Minimax Problem ◽  
Descent Method ◽  
Smoothing Parameter ◽  
Smoothing Method ◽  
Steepest Descent Method ◽  
Adaptive Smoothing ◽  
Ill Conditioning ◽  
Quasi Newton ◽  
Continuous Minimax

A simple and implementable two-loop smoothing method for semi-infinite minimax problem is given with the discretization parameter and the smoothing parameter being updated adaptively. We prove the global convergence of the algorithm when the steepest descent method or a BFGS type quasi-Newton method is applied to the smooth subproblems. The strategy for updating the smoothing parameter can not only guarantee the convergence of the algorithm but also considerably reduce the ill-conditioning caused by increasing the value of the smoothing parameter. Numerical tests show that the algorithm is robust and effective.

Adaptive Smoothing of Spectroscopic Data by a Linear Mean-Square Estimation

1984 ◽  
Vol 38 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Satoshi Kawata ◽  
Shigeo Minami
Keyword(s):  
Spectroscopic Data ◽  
Signal To Noise Ratio ◽  
Computation Time ◽  
Smoothing Method ◽  
Window Function ◽  
Mean Square ◽  
Least Mean Square ◽  
Adaptive Smoothing ◽  
Local Statistics ◽  
Convolution Algorithm

An adaptive smoothing method based on a least mean-square estimation is developed for noise filtering of spectroscopic data. The algorithm of this method is nonrecursive and shift-varying with the local statistics of data. The mean and the variance of the observed spectrum at an individual sampled point are calculated point by point from its local mean and variance. By this method, in the resultant spectrum, the signal-to-noise ratio is maximized at any local section of the entire spectrum. Experimental results for the absorption spectrum of ammonia gas demonstrate that this method distorts less amount of signal components than the conventional smoothing method based on the polynomial curve-fitting and suppresses noise components satisfactorily. The computation time of this algorithm is rather shorter than that of the convolution algorithm with seven weighting coefficients. The a priori information for the estimation of the signal by this method are: the variance of noise, which can be attainable in the experiment; and the window function which gives the local statistics. The investigation of various types of window functions shows that the selection of the window function does not directly affect the performance of adaptive smoothing.

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