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• W2893320574 abstract "The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as they proceed indirectly, via Cholesky decompositions or a block Gram-Schmidt procedure. For a highly ill-conditioned matrix, such approaches either break down in finite-precision arithmetic or result in significant loss of orthogonality. Although these issues can sometimes be addressed by regularization and iterative refinement, it would be more desirable to have an algorithm that avoids these detours and is numerically robust to ill-conditioning. In this work, we propose such an algorithm for HODLR matrices. It achieves accuracy by utilizing Householder reflectors. It achieves efficiency by utilizing fast operations in the HODLR format in combination with compact WY representations and the recursive QR decomposition by Elmroth and Gustavson. Numerical experiments demonstrate that our newly proposed algorithm is robust to ill-conditioning and capable of achieving numerical orthogonality down to the level of roundoff error." @default.
• W2893320574 created "2018-10-05" @default.
• W2893320574 creator A5044047041 @default.
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• W2893320574 date "2018-09-27" @default.
• W2893320574 modified "2023-09-27" @default.
• W2893320574 title "Fast QR decomposition of HODLR matrices" @default.
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