Abstract
We investigate the application of the LR Cholesky algorithm to symmetric hierarchical matrices, symmetric simple structured hierarchical matrices and symmetric hierarchically semiseparable (HSS) matrices. The data-sparsity of these matrices make the otherwise expensive LR Cholesky algorithm applicable, as long as the data-sparsity is preserved. We will see in an example that the ranks of the low rank blocks grow and the data-sparsity gets lost. We will explain this behavior by applying a theorem on the structure preservation of diagonal plus semiseparable matrices under LR Cholesky transformations. Therefore we have to give a new more constructive proof for the theorem. We will show that the structure of Hℓ-matrices is almost preserved and so the LR Cholesky algorithm is of almost quadratic complexity for Hℓ-matrices.
Original language | English |
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Pages (from-to) | 1150-1166 |
Number of pages | 17 |
Journal | Linear Algebra and Its Applications |
Volume | 439 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2013 |
Externally published | Yes |
Keywords
- Eigenvalues
- Hℓ-Matrices
- LR Cholesky algorithm
- Semiseparable matrices
- Symmetric hierarchical matrices
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics