A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map
In this paper we propose a quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map where the Newton method is used to solve an equivalent system of nonlinear equations. The semi-symmetric tensor is introduced to reveal the relation between ho...
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| Veröffentlicht in: | Journal of global optimization 2015-04, Vol.61 (4), p.627-641 |
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| container_title | Journal of global optimization |
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| creator | Ni, Qin Qi, Liqun |
| description | In this paper we propose a quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map where the Newton method is used to solve an equivalent system of nonlinear equations. The semi-symmetric tensor is introduced to reveal the relation between homogeneous polynomial map and its associated semi-symmetric tensor. Based on this relation a globally and quadratically convergent algorithm is established where the line search is inserted. Some numerical results of this method are reported. |
| doi_str_mv | 10.1007/s10898-014-0209-8 |
| format | Article |
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| issn | 0925-5001 1573-2916 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algorithms Computer Science Eigenvalues Eigenvectors Equivalence Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Nonlinear equations Operations Research/Decision Theory Optimization Polynomials Real Functions Studies Tensors |
| title | A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map |
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