LU decompositions of generalized diagonally dominant matrices |
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| Authors: | R. E. Funderlic M. Neumann R. J. Plemmons |
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| Affiliation: | (1) Mathematics and Statistics Research Department, Computer Sciences Division, Union Carbide Corporation, Nuclear Division, 37830 Oak Ridge, Tennessee, USA;(2) Department of Mathematics and Statistics, University of South Carolina, 29208 Columbia, South Carolina, USA;(3) Mathematics and Computer Science Departments, North Carolina State University, 27650 Raleigh, North Carolina, USA |
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| Abstract: | Summary Using the simple vehicle ofM-matrices, the existence and stability ofLU decompositions of matricesA which can be scaled to diagonally dominant (possibly singular) matrices are investigated. Bounds on the growth factor for Gaussian elimination onA are derived. Motivation for this study is provided in part by applications to solving homogeneous systems of linear equationsAx=0, arising in Markov queuing networks, input-output models in economics and compartmental systems, whereA or –A is an irreducible, singularM-matrix.This paper extends earlier work by Funderlic and Plemmons and by Varga and Cai.Research sponsored by the Applied Mathematical Sciences Research Program, Office of Energy Research, U.S. Department of Energy under contract W-7405-eng-26 with the Union Carbide CorporationResearch supported in part by the National Science Foundation under Grant No. MCS 8102114Research supported in part by the U.S. Army Research Office under contract no. DAAG 29-81-k-0132 |
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| Keywords: | AMS(MOS): 65F05 CR: 5.14 |
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