An Adaptive Algebraic Multigrid Algorithm for Low-Rank Canonical Tensor Decomposition
An Adaptive Algebraic Multigrid Algorithm for Low-Rank Canonical Tensor Decomposition
复制标题
低阶典型张量分解的自适应代数多重网格算法
DOI：
10.1137/110855934
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Killian Miller
中科院分区：
文献类型：
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作者：
H. Sterck;Killian Miller
针对较小的$R$值，提出了一种基于代数多重网格的新算法，用于计算张量的秩 - $R$规范分解。标准交替最小二乘法（ALS）被用作松弛方法。在一个自适应设置阶段构建转移算子和粗层级张量，该阶段结合了乘法校正和自举代数多重网格。通过基于完全近似格式的加法求解阶段计算精确解。数值试验表明，对于某些测试问题，当需要高精度时，我们的多层方法明显优于独立的ALS方法。
A new algorithm based on algebraic multigrid is presented for computing the rank-$R$ canonical decomposition of a tensor for small $R$. Standard alternating least squares (ALS) is used as the relaxation method. Transfer operators and coarse-level tensors are constructed in an adaptive setup phase that combines multiplicative correction and bootstrap algebraic multigrid. An accurate solution is computed by an additive solve phase based on the full approximation scheme. Numerical tests show that for certain test problems our multilevel method significantly outperforms standalone ALS when a high level of accuracy is required.