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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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An improved generalized Newton method for absolute value equations.

Jingmei Feng1, Sanyang Liu2

  • 1School of Mathematics and Statistics, Xidian University, Xi'an, 710126 China ; Department of Engineering Management, Shaanxi Radio and TV University, Xi'an, 710119 China.

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|July 28, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces an improved generalized Newton method for solving absolute value equations. The method demonstrates efficient global and local quadratic convergence for NP-hard problems.

Keywords:
Absolute value equationsGeneralized Newton’s methodGlobal and local convergence

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Area of Science:

  • Numerical Analysis
  • Optimization Theory

Background:

  • Absolute value equations represent a challenging class of NP-hard problems.
  • Existing methods may face limitations in efficiency and convergence for these equations.

Purpose of the Study:

  • To propose and analyze an improved generalized Newton method for solving absolute value equations.
  • To demonstrate the convergence properties and computational efficiency of the new method.

Main Methods:

  • Development of an improved generalized Newton iteration.
  • Theoretical analysis of global and local quadratic convergence.
  • Conducting numerical experiments to validate performance.

Main Results:

  • The proposed method achieves global and local quadratic convergence.
  • Numerical results confirm the method's efficiency and high accuracy.
  • The method is effective for absolute value equations where singular values of A exceed 1.

Conclusions:

  • The improved generalized Newton method is a viable and efficient approach for solving absolute value equations.
  • The theoretical convergence guarantees are supported by practical numerical performance.
  • This work contributes a valuable tool for tackling NP-hard absolute value equations.