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WIREs Computational Statistic variant ts of GE mo tions are carried out between adiacent rows only. which (when co reveals the rank of A, REFERENCES 2C. CE Th f the comhination of ohe 1967 NJ:Prentice-Hall 17 Moler CB Matriy img.1972,15-268-270. ith Fortran and pag Translated from the Latin originals (1821-1828)by Stewart GW. 18.D H GW.LIN Philadelphia, PA 9.Do I.Du Croz I.Duff Is Ham Trans Math Softw 1990,16:1-17. PA and Applied Mathematics:2002.ISBN:0-89871-521-0 69. 6.Golub GH,Van Loan CF.Matrix Computations.3rd 19.IBN0-01b 0-0- 8(paperback). 21.Gustayson FG.Recursion leads to automatic variable 7.Stewart GW.The deco ach to matrix 22. 8.Householder AS.The Theory of Matrices in Numeri Toledo S. York:964 190486 18:1065-1081. 23.Anderson E.Bai Z.Bischof CH.Blackford S.Demme 9 ongarra J,Du Croz Gre mmar 8:281-330. hia.PA for Ind Mathematics:1999,ISBN:0-89871-447-8. 24.Buttari A,Langou J,Kurzak J,Dongarra J.A class 11. Edel 12.Kray ritis C Mitrouli M.The of Donga rd GPU lin M M.Towards dens systems.Parallel Comput 2010,36:232-240. 26.Blackford LS.Choi I.Cleary A.D'Azevedo E.Demmel I ty for industrial and applied mathematics:1997 LV.T 1BN:0-89871-397-8. omput appl math Corrigendum in Comput App Math1998,98:177. Volume 3.Mayuune 2011 2011 John wiley sons.Inc 237WIREs Computational Statistics Gaussian elimination • variants of GE motivated by parallel computing, such as pairwise elimination, in which elimina￾tions are carried out between adjacent rows only, • analyzing the extent to which (when computed in floating point arithmetic) an LU factorization reveals the rank of A, • the sensitivity of the LU factors to perturbations in A. For more on these topics see Ref 5 and the references therein. REFERENCES 1. Lay-Yong L, Kangshen S. Methods of solving lin￾ear equations in traditional China. Hist Math 1989, 16:107–122. 2. Gauss CF. Theory of the Combination of Observa￾tions Least Subject to Errors. 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Philadelphia, PA: Society for Industrial and Applied Mathematics; 1999, ISBN:0-89871-447-8. 24. Buttari A, Langou J, Kurzak J, Dongarra J. A class of parallel tiled linear algebra algorithms for multicore architectures. Parallel Comput 2009, 35:38–53. 25. Tomov S, Dongarra J, Baboulin M. Towards dense linear algebra for hybrid GPU accelerated manycore systems. Parallel Comput 2010, 36:232–240. 26. Blackford LS, Choi J, Cleary A, D’Azevedo E, Demmel J, Dhillon I, Dongarra J, Hammarling S, Henry G, Petitet A, et al. ScaLAPACK Users’ Guide. Philadelphia, PA: Society for Industrial and Applied Mathematics; 1997, ISBN:0-89871-397-8. 27. Grigori L, Demmel JW, Xiang H. Communication Avoiding Gaussian Elimination. SC’08: Proceedings of the 2008 ACM/IEEE Conference on Supercomputing. Volume 3, May/June 2011  2011 John Wiley & Son s, In c. 237
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