Table 2.
Comparison of averaged error and mean count number for estimated rate constants of system 2 using algorithms 1 and 2.
| Δt | α\k | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|---|
| Algorithm 1 | |||||||
| 2 | 0.05 | MN | 18.29 | 7.53 | 9.8 | 12.7 | 14.23 |
| AE | 4.6211 | 4.4179 | 4.7138 | 4.2188 | 3.8119 | ||
| Same ∈k | MN | 2.69 | 2.07 | 2.16 | 1.93 | 1.93 | |
| AE | 4.7006 | 4.9603 | 4.8841 | 4.6833 | 4.7298 | ||
| Diff. ∈k | MN | 15.26 | 7.85 | 8.78 | 13.06 | 12.28 | |
| AE | 4.8295 | 4.5322 | 5.0418 | 4.7346 | 4.6069 | ||
| 5 | 0.05 | MN | 9.69 | 3.48 | 3.12 | 58.2 | 74.07 |
| AE | 4.1076 | 4.3243 | 4.1868 | 3.5311 | 3.5194 | ||
| Same ∈k | MN | 2.34 | 2.31 | 2.42 | 16.9 | 11.38 | |
| AE | 4.9862 | 4.7669 | 4.6716 | 3.8873 | 4.0017 | ||
| Diff. ∈k | MN | 25.72 | 8.14 | 10.45 | 25.8 | 174.88 | |
| AE | 4.0461 | 3.9583 | 3.7474 | 3.5655 | 3.6951 | ||
| Algorithm 2 | |||||||
| 2 | 0.05 | MN | 89.7 | 19.75 | 17.8 | 40.42 | 69.52 |
| AE | 4.0540 | 4.1339 | 4.1376 | 3.9696 | 3.9009 | ||
| Same ∈k | MN | 2.52 | 3.85 | 3.55 | 3.82 | 3.84 | |
| AE | 5.0456 | 4.6069 | 4.3666 | 4.5876 | 3.8958 | ||
| Diff. ∈k | MN | 197.49 | 15.05 | 22.09 | 36.85 | 94.24 | |
| AE | 3.8712 | 3.7934 | 4.3158 | 3.6485 | 3.5989 | ||
| 5 | 0.05 | MN | 138.14 | 30.52 | 46.66 | 98.87 | 377.66 |
| AE | 4.0258 | 3.7218 | 3.8258 | 3.8445 | 3.9205 | ||
| Same ∈k | MN | 21.67 | 11.34 | 11.17 | 26.65 | 59.64 | |
| AE | 4.0545 | 3.5715 | 4.1910 | 3.7252 | 3.8667 | ||
| Diff. ∈k | MN | 185.54 | 28.39 | 33.81 | 89.81 | 846.61 | |
| AE | 3.7810 | 3.6694 | 3.6939 | 3.9806 | 3.8515 | ||
Three strategies are used to choose the discrepancy tolerance α: a fixed value of α= 0.05; varying αvalues; and α= ∈kdenoted as same ∈k); varying αvalues that are smaller than ∈k (denoted as diff. ∈k).(AE:Averaged Error; MN: Mean count Number).