A cubically convergent method for solving the largest eigenvalue of a nonnegative irreducible tensor
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In this paper, we present a cubically convergent method for finding the largest eigenvalue of a nonnegative irreducible tensor. A cubically convergent method is used to solve an equivalent system of nonlinear equations which is transformed by the tensor eigenvalue problem. Due to particular structure of tensor, Chebyshev’s direction is added to the method with a few extra computation. Two rules are designed such that the descendant property of the search directions is ensured. The global convergence is proved by using the line search technique. Numerical results indicate that the proposed method is competitive and efficient on some test problems.
KeywordsCubic convergence Tensor eigenvalue Nonnegative irreducible tensor Chebyshev’s method
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This work was supported by the Jiangsu Innovation Program for Graduate Education KYZZ160163; the National Natural Science Foundation of China under Grants 11471159,11571169,61661136001; and the Natural Science Foundation of Jiangsu Province under Grant BK20141409.
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