کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4600301 | 1336843 | 2013 | 17 صفحه PDF | دانلود رایگان |
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.
Journal: Linear Algebra and its Applications - Volume 439, Issue 4, 15 August 2013, Pages 1150-1166