| Citation: |
Changfeng Ma, Yuhong Wu, Yajun Xie. THE NEWTON-BASED MATRIX SPLITTING ITERATIVE METHOD FOR SOLVING GENERALIZED ABSOLUTE VALUE EQUATION WITH NONLINEAR TERM[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 896-914. doi: 10.11948/20240198
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THE NEWTON-BASED MATRIX SPLITTING ITERATIVE METHOD FOR SOLVING GENERALIZED ABSOLUTE VALUE EQUATION WITH NONLINEAR TERM
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Abstract
A new Newton-based matrix splitting iterative method is proposed for solving generalized absolute value equation with nonlinear term. We give the global convergence of this method. Further some new convergence conditions are proposed when A = M - N is an H-compatible splitting. Numerical results indicate that the new Newton-based matrix splitting iterative method for solving generalized absolute value equation with nonlinear term is effective.
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References
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Changfeng Ma, Yuhong Wu, Yajun Xie. THE NEWTON-BASED MATRIX SPLITTING ITERATIVE METHOD FOR SOLVING GENERALIZED ABSOLUTE VALUE EQUATION WITH NONLINEAR TERM[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 896-914. doi: 10.11948/20240198
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Figure 1.
Selection of optimal parameters
$ \alpha^{'}, \beta $ -
Figure 2.
Convergence effect for Example 5.1.
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Figure 3.
Selection of optimal parameters
$ \alpha^{'}, \beta $ -
Figure 4.
Convergence effect for Example 5.2 (q=1;p=2).
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Figure 5.
Selection of optimal parameters
$ \alpha^{'}, \beta $ -
Figure 6.
Convergence effect for Example 5.2 (q=2;p=4).