TY  - JOUR
AB  - This paper establishes a new componentwise perturbation result for the Perron root of a non-negative and irreducible matrix. The error bound is independent of the angle between left and right Perron eigenvectors. It is shown that a known inverse iteration algorithm with new stopping criteria will have a small componentwise backward error, which is consistent with the perturbation result. Numerical experiments demonstrate that the accuracy of the Perron root computed by the proposed algorithm is, indeed, independent of the angle.
DA  - 1993
DO  - 10.1137/0614032
KW  - Nonnegative matrices
KW  - Componentwise perturbations
KW  - Perron root
KW  - Stable algorithms
KW  - Backward error
KW  - Sparse systems
LA  - eng
IS  - 2
M2  - 456
PY  - 1993
SN  - 0895-4798
SP  - 456-467
T2  - SIAM Journal on matrix analysis and applications
TI  - On accurate computations of the Perron root
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-17762255
Y2  - 2024-11-24T10:19:50
ER  -