A data structure for sparse qr and lu factorizations

Journal Article · Fri Jan 01 04:00:00 EST 1988 · SIAM J. Sci. Stat. Comput.; (United States)

DOI:https://doi.org/10.1137/0909008· OSTI ID:5341013

George, A; Liu, J; Ng, E

For a general m by n sparse matrix A, a new scheme is proposed for the structural representation of the factors of its sparse orthogonal decomposition by Householder transformations. The storage scheme is row-oriented and is based on the structure of the upper triangular factor obtained in the decomposition. The storage of the orthogonal matrix factor is particularly efficient in that the overhead required is only m+n items, independent of the actual number of nonzeros in the factor. The same scheme is applicable to sparse orthogonal factorization by Givens rotations, and also to the recent implementation of sparse Gaussian elimination with partial pivoting. Experimental results are provided to compare the sparse Gaussian elimination using the new storage scheme.

• Research Organization: Mathematical Sciences Section, Oak Ridge National Lab., Oak Ridge, TN 37831
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 5341013
• Journal Information: SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 9:1; ISSN SIJCD
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
BENCHMARKS
COMPARATIVE EVALUATIONS
COMPUTER CALCULATIONS
DATA
INFORMATION
MATHEMATICAL MODELS
MATRICES
NUMERICAL SOLUTION
ORTHOGONAL TRANSFORMATIONS
TRANSFORMATIONS