Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 }$.

References [Enhancements On Off] (What's this?)

  • [1] G. Buffoni and A. Galati, Matrici essenzialmente positive con inversa positiva, Boll. Un. Mat. Ital. (4) 10 (1974), 98–103 (Italian, with English summary). MR 0374165
  • [2] Ky Fan, Topological proofs for certain theorems on matrices with non-negative elements, Monatsh. Math. 62 (1958), 219–237. MR 0095856
  • [3] J. R. Rice, Numerical methods, software and analysis, McGraw-Hill, 1983.
  • [4] Yu. M. Svirezhev and D. O. Logofet, Stability of biological communities, “Mir”, Moscow, 1983. Translated from the Russian by Alexey Voinov [A. A. Voinov]. MR 723326
  • [5] Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F10, 15A09, 15A12, 15A48

Retrieve articles in all journals with MSC: 65F10, 15A09, 15A12, 15A48

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society