Maintaining LU Factors of a General Sparse Matrix.
STANFORD UNIV CA SYSTEMS OPTIMIZATION LAB
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The authors describe a set of procedures for computing and updating an LU factorization of a sparse matrix A, where A may be square possibly singular or rectangular. The procedures include a Markowitz factorization and a Bartels-Golub update, similar to those of Reid 1976, 1982. The updates provided are addition, deletion or replacement of a row or column of A, and rank-one modification. Previously, column replacement has been the only update available. Various design features of the implementation LUSOL are described, and computational comparisons are made with the LA05 and MA28 packages of Reid 1976 and Duff 1977. Keywords Sparse matrix LU factors, matrix factorization, matrix updates, rank-one modification, Fortran software, lower and upper triangular.
- Numerical Mathematics