Accurate computation of the smallest eigenvalue of a diagonally dominant M-matrix
Mathematics of Computation
| Hi-index | 0.01 |
A computation of the smallest eigenvalue and the corresponding eigenvector of an irreducible nonsingular M-matrix $A$ is considered. It is shown that if the entries of $A$ are known with high relative accuracy, the smallest eigenvalue and each component of the corresponding eigenvector will be determined to high relative accuracy. A known inverse iteration algorithm with new stopping criterion is presented to compute them. Under certain assumptions, the algorithm will have a small componentwise backward error, which is consistent with the perturbation results.