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Published in:
2015 | OriginalPaper | Chapter
Eigenvalue Problems
Author : Wolfgang Hackbusch
Published in: Hierarchical Matrices: Algorithms and Analysis
Publisher: Springer Berlin Heidelberg
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In this chapter, we consider various numerical methods for solving the eigenvalue problem and the application of hierarchical matrix techniques. After the introduction in Section 13.1, we discuss the LR and QR methods in Section 13.2, the vector iteration and Krylov methods in Section 13.3, and the preconditioned inverse iteration in Section 13.4. Furthermore, we consider the bisection method in Section 13.5 and the divide-and-conquer method in Section 13.6. Quite another approach is the computation of an eigenvalue distribution in Section 13.7. Finally, spectral projections are studied in Section 13.8.