M-matrices leading to semiconvergent splittings |
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Authors: | R.J. Plemmons |
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Affiliation: | Department of Computer Science and Mathematics The University of Tennessee Knoxville, Tennessee 37916, USA |
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Abstract: | An M-matrix as defined by Ostrowski is a matrix that can be split into A = sI ? B, s > 0, B ? 0 with s ? ρ(B), the spectral radius of B. M-matrices with the property that the powers of T = (1/s)B converge for some s are studied and are characterized here in terms of the nonnegativity of the group generalized inverse of A on the range space of A, extending the well-known property that A? 1 ? 0 whenever A is nonsingular. |
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