Exact(10)
However, the convergence and convergence rate of the Newton iterations depend heavily on the selections of the initial iterative function and iterative step length.
We prove that, under proper assumptions, this significantly improves the convergence rate of the initial iterative method.
The initial iterative value (t = 1).
Input the initial iterative point and penalty parameter into the AHT algorithm.
Especially, the initial iterative solutions in the monotone iterative algorithms can be obtained directly by solving two discrete linear complementarity problems without any knowledge of the exact solution.
We employ (|e u^{k},rho_{k})|leq10^{-7}) as the stopping criterion and choose (u^{0}=0) as the initial iterative points.
Similar(50)
Since an initial iteration in the monotone iterative method is either an upper or lower solution, which can be constructed directly from the difference equation without any knowledge of the exact solution, this method simplifies the search for the initial iteration as is often required in the Newton method.
Simultaneously, we choose the same initial iterative points (x^{0}=mathbf{1}), (y^{0}=lambda^{0}=mandbf{0}), and the stopping criterion (|hat{w}^{k}-w^{k}|leqepsilon) in all methods.
In this section, we present some experiments of the Newton method to solve the p-Laplace equation based on two different initial iterative functions so as to validate the conclusion of theoretical analysis in the preceding section.
According to the well-posed condition, an effective initial iterative function is presented.
After item generation and initial iterative changes to the PRUNE, a larger potential instrument was tested on respondents.
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