Hierarchical Kronecker tensor-product approximations

被引：79
作者：
Hackbusch, W. [1 ]
Khoromskij, B.N. [1 ]
Tyrtyshnikov, E.E. [2 ]
机构：
[1] Max-Planck-Institute for Mathematics in the Sciences, D-04103 Leipzig
[2] Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow GSP-1
来源：
Journal of Numerical Mathematics | 2005年 / 13卷 / 02期
关键词：
BEM; Hierarchical matrices; Integral equations; Kronecker products; Low-rank matrices; Multi-dimensional matrices; Tensors;
D O I：
10.1163/1569395054012767
中图分类号：
学科分类号：
摘要：
The goal of this work is the presentation of some new formats which are useful for the approximation of (large and dense) matrices related to certain classes of functions and nonlocal (integral, integro-differential) operators, especially for high-dimensional problems. These new formats elaborate on a sum of few terms of Kronecker products of smaller-sized matrices (cf. [37,38]). In addition to this we need that the Kronecker factors possess a certain data-sparse structure. Depending on the construction of the Kronecker factors we are led to so-called 'profile-low-rank matrices' or hierarchical matrices (cf. [18,19]). We give a proof for the existence of such formats and expound a gainful combination of the Kronecker-tensor-product structure and the arithmetic for hierarchical matrices. © VSP 2005.
引用
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页码：119 / 156
页数：37
相关论文
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