MIQR
swMATH ID:  7242 
Software Authors:  Li, Na; Saad, Yousef 
Description:  MIQR: a multilevel incomplete QR preconditioner for large sparse leastsquares problems
This paper describes a multilevel incomplete QR factorization for solving large sparse leastsquares problems. The algorithm builds the factorization by exploiting structural orthogonality in general sparse matrices. At any given step, the algorithm finds an independent set of columns, i.e., a set of columns that have orthogonal patterns. The other columns are then block orthogonalized against columns of the independent set, and the process is repeated recursively for a certain number of levels on these remaining columns. The final level matrix is processed with a standard QR or incomplete QR factorization. Dropping strategies are employed throughout the levels in order to maintain a good level of sparsity. A few improvements to this basic scheme are explored. Among these is the relaxation of the requirement of independent sets of columns. Numerical tests are proposed which compare this scheme with the standard incomplete QR preconditioner, the robust incomplete factorization preconditioner, and the algebraic recursive multilevel solver (on normal equations). 
Homepage:  http://dl.acm.org/citation.cfm?id=1132367.1151269 
Keywords:  multilevel incomplete QR factorization; CGLS; QR factorization; orthogonal factorization; preconditioning; iterative methods; large leastsquares problems; normal equations; numerical examples; algorithm 
Related Software:  SparseMatrix; SuiteSparseQR; HSL; SuitSparseQR; LSQR; CRAIG; LSMR; CIMGS; HSL_MI28; CUTEst; HSL_MA87; MUMPS; CHOLMOD; SYMILDL; HSL_MA97; WSMP; MA57; ParILUT; hypre; qr_mumps 
Cited in:  12 Documents 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

MIQR: a multilevel incomplete QR preconditioner for large sparse leastsquares problems. Zbl 1113.65036 Li, Na; Saad, Yousef 
2006

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top 5
Cited by 20 Authors
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top 5
Cited in 7 Serials
Cited in 4 Fields
12  Numerical analysis (65XX) 
1  Combinatorics (05XX) 
1  Linear and multilinear algebra; matrix theory (15XX) 
1  Partial differential equations (35XX) 