A modified Newton's method for best rank-one approximation to tensors

作者：Chang, Jingya; Sun, Wenyu^*; Chen, Yannan

来源：Applied Mathematics and Computation, 2010, 216(6): 1859-1867.

DOI：10.1016/j.amc.2009.12.019

• Numerical multilinear algebra
• Tensor computation
• Rank-one approximation
• Modified Newton's method
• Projective direction

In this paper, a modified Newton's method for the best rank-one approximation problem to tensor is proposed. We combine the iterative matrix of Jacobi-Gauss-Newton (JGN) algorithm or Alternating Least Squares (ALS) algorithm with the iterative matrix of GRQ-Newton method, and present a modified version of GRQ-Newton algorithm. A line search along the projective direction is employed to obtain the global convergence. Preliminary numerical experiments and numerical comparison show that our algorithm is efficient.

• 出版日期2010-5-15
• 单位南京林业大学; 南京师范大学