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Mathematics of Computation

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Monotonicity and iterative approximations involving rectangular matrices

Author: Robert J. Plemmons
Journal: Math. Comp. 26 (1972), 853-858
MSC: Primary 65F20
MathSciNet review: 0315882
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Abstract: A new characterization of row-monotone matrices is given and is related to the Moore-Penrose generalized inverse. The $ M$-matrix concept is extended to rectangular matrices with full column rank. A structure theorem is provided for all matrices $ A$ with full column rank for which the generalized inverse $ {A^ + } \geqq 0$. These results are then used to investigate convergent splittings of rectangular matrices in relation to iterative techniques for computing best least squares solutions to rectangular systems of linear equations.

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Keywords: Convergent splitting, generalized inverse, iterative solutions to systems of linear equations, (rectangular) $ M$-matrix, (row-) monotone matrix
Article copyright: © Copyright 1972 American Mathematical Society

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