| Affiliation: | Department of Industrial and Manufacturing Systems Engineering, University of Windsor, Windsor, Ontario, Canada N9B 3P4 ; Fakultaet fuer Mathematik, Technishe Universitaet Chemnitz, Reichenhainer Str. 41, 09126 Chemnitz, Germany ; Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027 |
| Abstract: | If each off-diagonal entry and the sum of each row of a diagonally dominant  -matrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision. Rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms. |
