| Title:
|
Schur complements of matrices with acyclic bipartite graphs |
| Type:
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Journal articleJournal article |
| Participant(s):
|
Technical University of Denmark
Forfatter:
Olesky, D.D.
Technical University of Denmark
Forfatter:
van den Driessche, P.
Technical University of Denmark
|
| Abstract:
|
Bipartite graphs are used to describe the generalized Schur complements of real matrices having nos quare submatrix with two or more nonzero diagonals. For any matrix A with this property, including any nearly reducible matrix, the sign pattern of each generalized Schur complement is shown to be determined uniquely by the sign pattern of A. Moreover, if A has a normalized LU factorization A = LU, then the sign pattern of A is shown to determine uniquely the sign patterns of L and U, and ( with the standard LU factorization) of L-1 and, if A is nonsingular, of U-1. However, if A is singular, then the sign pattern of the Moore-Penrose inverse U dagger may not be uniquely determined by the sign pattern of A. Analogous results are shown to hold for zero patterns. |
| Published:
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in journal: Electronic Journal of Linear Algebra (ISSN: 1081-3810), vol: 14, pages: 2-11, 2005 |
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