Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions
Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions
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高维椭圆解算子的 Quantics-TT 逼近
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
I. Oseledets
中科院分区：
文献类型：
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作者：
B. Khoromskij;I. Oseledets
在本文中，我们提出了用于高维椭圆方程数值求解的 Quantics-TensorTrain (QTT) 方法的数值分析。 Frobenius 范数中的 e 精确解可以用复杂度 O(d log e−1) 计算，其中 d ≥ 2 是空间维度，q ≥ 2 是某个固定常数。这似乎是 d 维数值模拟中预期的近乎最优的渐近计算成本。 AMS 科目分类：65F50、65F30、46B28、47A80
In the present paper, we present the numerical analysis of the Quantics-TensorTrain (QTT) methods for numerical solution of the elliptic equations in higher dimensions. The e-accurate solutions in the Frobenius norm can be computed with the complexity O(d log e−1), where d ≥ 2 is the spatial dimension, and q ≥ 2 is some fixed constant. This seems to be the nearly optimal asymptotical computational cost to be expected in the d-dimensional numerical simulations. AMS Subject Classification: 65F50, 65F30, 46B28, 47A80