Preprint No. MPIMD/12-05

Title: The LR Cholesky Algorithm for Symmetric Hierarchical Matrices

Author(s): Peter Benner, Thomas Mach


Date: 2012-02-28


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 data-sparsity of hierarchical matrices is not well preserved.

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 ℋ-matrices is almost preserved and so the LR Cholesky algorithm is of almost quadratic complexity for ℋ-matrices.


author = {Peter Benner and Thomas Mach},
title = {The LR Cholesky Algorithm for Symmetric Hierarchical Matrices},
number = {MPIMD/12-05},
month = feb,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

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