For a general third-order tensor $\mathcal{A}\in\mathbb{R}^{n\times n\times n}$ the paper studies two closely related problems, the SVD-like tensor decomposition and the (approximate) tensor diagonalization. We develop the alternating least squares Jacobi-type algorithm that maximizes the squares of the diagonal entries of $\mathcal{A}$. The algorithm works on $2\times2\times2$ subtensors such that in each iteration the sum of the squares of two diagonal entries is maximized. We show how the rotation angles are calculated and prove the convergence of the algorithm. Different initializations of the algorithm are discussed, as well as the special cases of symmetric and antisymmetric tensors. The algorithm can be generalized to work on the higher-order tensors.

翻译：对于一般的三阶高压 $mathcal{A ⁇ in\mathbb{R ⁇ n\timen\time n}, 纸张研究两个密切相关的问题, SVD 类似 shor 分解和(近似) Exqor diagal 。 我们开发了交替最小正方形的雅各布式算法, 使对角条目的正方形最大化 $\ mathcal{A}。 算法使用2\ times2\time2 subs2 subtors, 这样在每次迭代法中, 两个对角条目的方形和正方形是最大化的。 我们展示了如何计算和证明算法的趋同。 讨论了不同的算法初始化, 以及对称和反对称强力的特例。 算法可以普遍化为高阶数控法。