A Non-Monotone Quasi-Newton Algorithm for Computing Z-Eigenvalues of Symmetric Tensors
The tensor eigenvalues problem has attracted people's attention in recent years,which has important applications in mathematical statistics and signal processing especially Z-eigenvalues of symmetric tensor.According to the equivalence transformation between Z-eigenvalues of symmetric tensor and nonlinear equations.Using the non-monotone line search,a convergent Quasi-Newton algorithm is proposed for computing Z-eigenvalues of a symmetric tensor.The algorithm does not require the calculation and storage of Jacobian matrices,which can improve the efficiency of computing.During the iteration process,the positive determinism of the Quasi-Newton matrix is guaranteed.Under appropriate conditions,global convergence of the proposed algorithm is established.Numerical experiments are listed to illustrate the efficiency of the proposed method.
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