The totally pivoted LU decomposition is the most stable among all LU-like factorizations, but unfortunately also computationally expensive, and not amendable to exploit level 3 BLAS operations. In this contribution, we derive a block organized LU factorization, in which at each step of the algorithm a totally pivoted LU decomposition is applied to a sub-block of the current matrix. An optimal exploitation of the matrix-matrix products results in a significantly improved performance.
Dimiccoli, L, Truyen, B & Cornelis, J 2006, A block quasi-totally pivoted LU decomposition. in Proceedings SIAM 2006 Annual Meeting. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, pp. 224-224, SIAM 2006 Annual Meeting
, Boston, Massachusetts, United States, 10/07/06.
Dimiccoli, L., Truyen, B., & Cornelis, J. (2006). A block quasi-totally pivoted LU decomposition. In Proceedings SIAM 2006 Annual Meeting (pp. 224-224). Society for Industrial and Applied Mathematics (SIAM).
@inproceedings{33cdd87008094b84b81b19bfe634f0a6,
title = "A block quasi-totally pivoted LU decomposition",
abstract = "The totally pivoted LU decomposition is the most stable among all LU-like factorizations, but unfortunately also computationally expensive, and not amendable to exploit level 3 BLAS operations. In this contribution, we derive a block organized LU factorization, in which at each step of the algorithm a totally pivoted LU decomposition is applied to a sub-block of the current matrix. An optimal exploitation of the matrix-matrix products results in a significantly improved performance.",
keywords = "LU decomposition, block factorization",
author = "Luca Dimiccoli and Bart Truyen and Jan Cornelis",
year = "2006",
month = jul,
day = "10",
language = "English",
pages = "224--224",
booktitle = "Proceedings SIAM 2006 Annual Meeting",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
note = "SIAM 2006 Annual Meeting<br/> ; Conference date: 10-07-2006 Through 14-07-2006",
}