In this paper, a quarticly convergent method is proposed for solving a system of nonlinear equations, which is a three-step iterative method. This method is used to find the largest H eigenvalue of irreducible nonnegative tensor and the Z eigenvalues of general tensors, where its computational complexity is slightly greater than Newton method. Due to the particular structure of the problem, the computation of three order tensor and four order tensor are implicit, and a economic computing scheme is given in the algorithm. The global and quartic convergence of the new method are proved. Numerical results indicate that the proposed method is competitive and efficient on some tensor problems.
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