In this paper, we show that for a symmetric tensor, its best symmetric rank-1 approximation is its best rank-1 approximation. Based on this result, a positive lower bound for the best rank-1 approximation ratio of a symmetric tensor is given. Furthermore, a higher order polynomial spherical optimization problem can be reformulated as a multilinear spherical optimization problem. Then, we present a modified power algorithm for solving the homogeneous polynomial spherical optimization problem. Numerical results are presented, illustrating the effectiveness of the proposed algorithm.
- Power algorithm
- Symmetric tensor
- The best rank-1 approximation
- The best symmetric rank-1 approximation
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