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تسجيل مستخدم جديدInexact Newton Method for M-Tensor Equations
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We first investigate properties of M-tensor equations. In particular, we show that if the constant term of the equation is nonnegative, then finding a nonnegative solution of the equation can be done by finding a positive solution of a lower dimensional M-tensor equation. We then propose an inexact Newton method to find a positive solution to the lower dimensional equation and establish its global convergence. We also show that the convergence rate of the method is quadratic. At last, we do numerical experiments to test the proposed Newton method. The results show that the proposed Newton method has a very good numerical performance.
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We are concerned with the tensor equations whose coefficient tensor is an M-tensor. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend the method
to solve the equation with a nonnegative constant term and establish its convergence. At last, we do numerical experiments to test the proposed methods. The results show that the proposed method is quite efficient.
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