On this basis, an improved generalized Newton algorithm is proposed by adding a dynamic step size, and the accuracy of the solution is of. Mangasarian proposed a generalized Newton method for solving AVEs ( 1) when it has a unique solution then 100 AVEs ( 1) of 1000 dimensions generated randomly are used to test effectiveness of this method, and the accuracy is up to. Next, many scholars began to design effective algorithms to solve equations with different types of solutions. In, some theoretical conclusions about the solutions of AVEs ( 1) are given, and the sufficient conditions for the existence of unique solutions, nonnegative solutions, solutions, and no solutions are given for the first time. This paper mainly designed a three-step iterative algorithm to solve the absolute value equations (AVEs) of the following type: where, , and indicates the absolute value. In the last few decades, the system of absolute value equations has been recognized as a kind of NP-hard and nondifferentiable problem, which can be equivalent to many mathematical problems, such as generalized linear complementarity problem, bilinear programming problem, knapsack feasibility problem, traveling agent problem, etc…However, compared with the above problems, it has the characteristics of simple structure and easy solution, which attracts much attention. Numerical examples show that this algorithm has high accuracy and fast convergence speed for solving the system of nonlinear equations. The proposed method has the global linear convergence and the local quadratic convergence. In this paper, we transform the problem of solving the absolute value equations (AVEs) with singular values of greater than 1 into the problem of finding the root of the system of nonlinear equation and propose a three-step algorithm for solving the system of nonlinear equation.
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