CALU
swMATH ID:  6433 
Software Authors:  Grigori, Laura; Demmel, James W.; Xiang, Hua 
Description:  CALU: A communication optimal LU factorization algorithm
The authors discussed CALU, a communication avoiding LU factorization algorithm. The main part of the paper focuses on showing that CALU is stable in practice. It is also shown that CALU minimizes communications. The paper is organized as follows. Section 1 is an introduction. In Section 2 presents the algebra of CALU and the new tournament pivoting scheme. Section 3 is devoted to the stability of CALU. It describes similarities between GEPP and CALU and upper bounds of the growth factor of CALU. Experimental results for random matrices and several special matrices showing that CALU is stable in practice are also presented. In Section 4 two alternative approaches for solving linear systems of LUlike factorization are discussed. In Section 5 parallel and sequential CALU algorithms and their performance models are presented. Section 6 recalls lower bounds on communications and shows that CALU attains them. Finally, Section 7 concludes the paper. 
Homepage:  http://www.netlib.org/lapack/lawnspdf/lawn226.pdf 
Keywords:  LU factorization; communication optimal algorithm; numerical stability; parallel computation; numerical examples; tournament pivoting scheme; random matrices 
Related Software:  SparseMatrix; LAPACK; ScaLAPACK; SUMMA; POOCLAPACK; LINPACK; BLAS; CSparse; SuiteSparseQR; CHOLMOD; SuperLU; PARDISO; HSL; Regularization tools; SuperLUDIST; METIS; mctoolbox; Algorithm 97; Pochoir; CTF 
Referenced in:  11 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

CALU: A communication optimal LU factorization algorithm. Zbl 1242.65089 Grigori, Laura; Demmel, James W.; Xiang, Hua 
2011

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top 5
Referenced by 22 Authors
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top 5
Referenced in 6 Serials
Referenced in 5 Fields
11  Numerical analysis (65XX) 
3  Linear and multilinear algebra; matrix theory (15XX) 
2  Computer science (68XX) 
1  Combinatorics (05XX) 
1  Number theory (11XX) 