Advertisement
Published in:
2015 | OriginalPaper | Chapter
Miscellaneous Supplements
Author : Wolfgang Hackbusch
Published in: Hierarchical Matrices: Algorithms and Analysis
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
This chapter is devoted to six different topics. Section 9.1 concerns the solution of linear systems. Since the $$\mathcal{H}$$ -matrix technique allows us to compute the approximate LU decomposition, this approximation can be used as a perfect preconditioner in the iterative solution. The hierarchical LU decomposition of sparse matrices can be improved by the choice of a special ternary cluster tree (see Section 9.2). Section 9.3 introduces the weak admissibility which can be useful in particular cases. The cross approximation, explained in Section 9.4, is an important algorithm for the efficient computation of low-rank approximations. A fundamential question is the approximability by an $$\mathcal{H}$$ -format. Some criteria are discussed in Section 9.5. The efficient updating after a local grid refinement is touched upon in Section 9.6.