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 (2009). Given mth-order, n-dimensionalreal-valued symmetric tensors A and B, the goal is to find $\lambda \in R$ and$x \in R^n$, $x \neq 0$, such that $Ax^{m-1} = \lambda Bx^{m-1}$. Differentchoices for B yield different versions of the tensor eigenvalue problem. Wepresent our generalized eigenproblem adaptive power method (GEAP) method forsolving the problem, which is an extension of the shifted symmetrichigher-order power method (SS-HOPM) for finding Z-eigenpairs. A major drawbackof SS-HOPM was that its performance depended in choosing an appropriate shift,but our GEAP method also includes an adaptive method for choosing the shiftautomatically.
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机译：在过去的十年中，已经提出了几种张量本征对定义，但是在Changs，Pearson和Zhang（2009）引入的广义张量本征对框架下可以统一这些定义。给定m阶，n维实值对称张量A和B，目标是找到$ \ lambda \ in R $和$ x \ in R ^ n $，$ x \ neq 0 $，使得$ Ax ^ {m-1} = \ lambda Bx ^ {m-1} $。 B的不同选择会产生张量特征值问题的不同版本。我们提出了用于解决该问题的广义本征问题自适应幂方法（GEAP），它是用于查找Z本征对的移位对称高阶幂方法（SS-HOPM）的扩展。 SS-HOPM的主要缺点在于其性能取决于选择合适的换档，但是我们的GEAP方法还包括一种自动选择换档的自适应方法。
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