Timeline for Bounds on $\|(P+\Delta)^n - P^n\|_F$ for stochastic matrices
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 18, 2018 at 9:33 | comment | added | Federico Poloni | The error is $O(\lambda_2^k)$. Look up "power method" / "power iteration". | |
| Jun 18, 2018 at 9:03 | comment | added | mfrt | If we have access to this $\lambda_2$ (and its algebraic multiplicity), what is the convergence rate to the Perron vector ? Is this an exact bound or a $O(\ldots)$ ? | |
| Jun 17, 2018 at 15:12 | comment | added | Federico Poloni | @mfrt You can't say anything in general. They depend on the second largest eigenvalue $\lambda_2$ of $P$ (resp. $P+\Delta$), which requires some work to compute, and they can be arbitrarily slow if $\lambda_2 \approx 1$. | |
| Jun 17, 2018 at 14:21 | comment | added | mfrt | What are general convergence rates to the Perron vector if we suppose $P$ and $P+\Delta$ are both irreductible and aperiodic ? | |
| Jun 17, 2018 at 13:26 | history | answered | Federico Poloni | CC BY-SA 4.0 |