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Computing row and column counts for sparse QR and LU factorization

Journal Article · · BIT Numerical Mathematics
 [1]; ; ;
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We present algorithms to determine the number of nonzeros in each row and column of the factors of a sparse matrix, for both the QR factorization and the LU factorization with partial pivoting. The algorithms use only the nonzero structure of the input matrix, and run in time nearly linear in the number of nonzeros in that matrix. They may be used to set up data structures or schedule parallel operations in advance of the numerical factorization. The row and column counts we compute are upper bounds on the actual counts. If the input matrix is strong Hall and there is no coincidental numerical cancellation, the counts are exact for QR factorization and are the tightest bounds possible for LU factorization. These algorithms are based on our earlier work on computing row and column counts for sparse Cholesky factorization, plus an efficient method to compute the column elimination tree of a sparse matrix without explicitly forming the product of the matrix and its transpose.
Research Organization:
Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
Sponsoring Organization:
USDOE Director. Office of Science. Office of Advanced Scientific Computing Research. Mathematical Information and Computational Sciences Division, Lockheed Martin Energy Research Corporation, Applied Mathematical Research Program Contract DE-AC05-96OR22464; Defense Advanced Research Projects Agency Contract DABT63-95-C-0087 (US)
DOE Contract Number:
AC03-76SF00098
OSTI ID:
834431
Report Number(s):
LBNL--47372
Journal Information:
BIT Numerical Mathematics, Journal Name: BIT Numerical Mathematics Journal Issue: 4 Vol. 41
Country of Publication:
United States
Language:
English

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Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
CANCELLATION
FACTORIZATION
SCHEDULES
SPARSE FACTORIZATION QR LU ROW COUNT COLUMN COUNT
TREES