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Mathematics of Computation

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Nonnegative and skew-symmetric perturbations of a matrix with positive inverse

Author: Giuseppe Buffoni
Journal: Math. Comp. 54 (1990), 189-194
MSC: Primary 65F10; Secondary 15A09, 15A12, 15A48
MathSciNet review: 995208
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Abstract: Let A be a nonsingular matrix with positive inverse and B a non-negative matrix. Let the inverse of $ A + vB$ be positive for $ 0 \leq v < {v^ \ast } < + \infty $ and at least one of its entries be equal to zero for $ v = {v^ \ast }$; an algorithm to compute $ {v^ \ast }$ is described in this paper. Furthermore, it is shown that if $ A + {A^{\text{T}}}$ is positive definite, then the inverse of $ A + v(B - {B^{\text{T}}})$ is positive for $ 0 \leq v < {v^ \ast }$.

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Article copyright: © Copyright 1990 American Mathematical Society

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