AN ADAPTIVE SHIFTED POWER METHOD FOR COMPUTING GENERALIZED TENSOR EIGENPAIRS

作者：Kolda Tamara G^*; Mayo Jackson R

来源：SIAM Journal on Matrix Analysis and Applications, 2014, 35(4): 1563-1581.

DOI：10.1137/140951758

• tensor eigenvalues
• E-eigenpairs
• Z-eigenpairs
• l(2)-eigenpairs
• generalized tensor eigenpairs
• shifted symmetric higher-order power method
• SS-HOPM
• generalized eigenproblem adaptive power method
• GEAP

Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang [J. Math. Anal. Appl., 350 (2009), pp. 416-422]. Given mth-order, n-dimensional real-valued symmetric tensors A and B, the goal is to find lambda is an element of R and x is an element of R-n, x not equal 0 such that Ax(m-1) = lambda Bx(m-1). Different choices for B yield different versions of the tensor eigenvalue problem. We present our generalized eigenproblem adaptive power (GEAP) method for solving the problem, which is an extension of the shifted symmetric higher-order power method (SS-HOPM) for finding Z-eigenpairs. A major drawback of SS-HOPM is that its performance depended on choosing an appropriate shift, but our GEAP method also includes an adaptive method for choosing the shift automatically.

• 出版日期2014