Black Box Low Tensor-Rank Approximation Using Fiber-Crosses
Black Box Low Tensor-Rank Approximation Using Fiber-Crosses
复制标题
使用光纤交叉的黑盒低张量阶近似
DOI：
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复制
发表时间：
2009
期刊：
影响因子：
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通讯作者：
W. Hackbusch
中科院分区：
文献类型：
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作者：
Mike Espig;L. Grasedyck;W. Hackbusch
在本文中，我们引入了一种在高维d中近似张量a的黑盒型算法。该算法自适应地确定需要计算或读取的张量项的位置，并使用这些（少量）项构建一个低秩张量近似X，使a和X在所选位置之间的距离最小化。不需要全张量A，只需要在几个位置对A求值。最小化问题采用牛顿法求解，该方法需要对黑森量进行计算和评价。出于效率的考虑，这些位置位于张量的纤维交叉上，以便可以以需要复杂度为的数据稀疏形式组装和评估Hessian
AbstractIn this article we introduce a black box type algorithm for the approximation of tensors A in high dimension d. The algorithm adaptively determines the positions of entries of the tensor that have to be computed or read, and using these (few) entries it constructs a low rank tensor approximation X that minimizes the ℓ2-distance between A and X at the chosen positions. The full tensor A is not required, only the evaluation of A at a few positions. The minimization problem is solved by Newton’s method, which requires the computation and evaluation of the Hessian. For efficiency reasons the positions are located on fiber-crosses of the tensor so that the Hessian can be assembled and evaluated in a data-sparse form requiring a complexity of
$mathcal{O}(Pd)$
, where P is the number of fiber-crosses and d the order of the tensor.
影响因子：
2.1
作者：
R. Ramlau;Gerd Teschke;M. Zhariy
通讯作者：
R. Ramlau;Gerd Teschke;M. Zhariy