Here we provide a summary and detailed results for a comparison of minimizers in Mantid when using weights in the cost function. For an explanation of the comparison approach and the results obtained when not using weights see the General comparison of minimizers. In the results presented here the cost function used is least squares and weigths are defined from input observational error estimates. See the general concept page on fitting for an explanation on how the error estimates are used in the least squares cost function. This cost function is named in the list of cost functions available in Mantid as “Least squares”. It is the default cost function in Mantid and the most commonly used for neutron data.
For the Neutron data problems true observational errors are used as weights, as commonly done in Mantid. As the NIST and CUTEst problems do not include measurement errors, assuming that these datasets would represent data from a typical Mantid workspace we introduce observational error estimates calculated as the square root of the observations.
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| NIST, “lower” difficulty | 4.051 | 3.009 | 3.009 | 1 | 1 | 1 | 1.001 | 6.453 | 1 |
| NIST, “average” difficulty | 215.2 | 27.14 | 25.43 | 1.001 | 1 | 1 | 15.12 | 203.2 | 1 |
| NIST, “higher” difficulty | 26.92 | 11.91 | 5.804 | 1.005 | 1 | 1.006 | 6.393 | 40.18 | 1.001 |
| CUTEst | 36.53 | 10.1 | 9.345 | 1.579e+05 | 2.464 | 5315 | 14.31 | 58.03 | 1 |
| Neutron data | 1.667 | 1.566 | 1.643 | 1 | 1 | 1 | 2.334 | 3.546 | 1 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| Misra1a 1 | 152.6 | 151.7 | 151.7 | 1 | 1 | 1 | 1.001 | 151.7 | 1 |
| Misra1a 2 | 2.233 | 2.266 | 2.266 | 1 | 1 | 1 | 1.001 | 2.265 | 1 |
| Chwirut2 1 | 1.08 | 1.043 | 1.001 | 1 | 1 | 1 | 1.049 | 1.081 | 1 |
| Chwirut2 2 | 1.004 | 1 | 1 | 1 | 1 | 1 | 1.247 | 1.005 | 1 |
| Chwirut1 1 | 1.134 | 1.11 | 1.006 | 1.285 | 1.012 | 1.012 | 1 | 1.132 | 1.012 |
| Chwirut1 2 | 1.023 | 1 | 1.011 | 1.012 | 1.012 | 1.012 | 1.087 | 1.024 | 1.012 |
| Lanczos3 1 | 1.683e+06 | 8.746e+04 | 8.828e+04 | 1 | 1 | 1 | 1.833e+05 | 1.191e+06 | 1 |
| Lanczos3 2 | 1.982e+05 | 5.844e+04 | 5.685e+04 | 1.241 | 1.241 | 1 | 3540 | 1.866e+05 | 1.241 |
| Gauss1 1 | 5.637 | 5.596 | 5.596 | 1 | 1 | 1 | 1 | 5.637 | 1 |
| Gauss1 2 | 9.281 | 1.077 | 1.027 | 1 | 1 | 1 | 1.032 | 9.278 | 1 |
| Gauss2 1 | 2.465 | 7.338 | 7.338 | 1 | 1 | 1 | 1 | 7.269 | 1 |
| Gauss2 2 | 2.151 | 3.752 | 3.752 | 1 | 1 | 1 | 1 | 3.404 | 1 |
| DanWood 1 | 73.76 | 1 | 1.002 | 1 | 1 | 1 | 1.012 | 53.75 | 1 |
| DanWood 2 | 1.231 | 1.005 | 1.005 | 1.005 | 1.005 | 1.005 | 1 | 2.04 | 1.005 |
| Misra1b 1 | 101.2 | 97.62 | 97.62 | 1 | 1 | 1 | 1 | 97.58 | 1 |
| Misra1b 2 | 15.72 | 15.44 | 15.44 | 4.476e+05 | 1 | 1 | 1 | 15.44 | 1 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| Kirby2 1 | 309.1 | 13.83 | 13.49 | 1 | 1 | 1 | 210.8 | 285.4 | 1 |
| Kirby2 2 | 1.042 | 1 | 1.106 | 1.042 | 1.042 | 1.042 | 4.37 | 70.06 | 1.042 |
| Hahn1 1 | 2.788e+04 | 2.666e+04 | 74.31 | 472.2 | 15.15 | 19.09 | 280.6 | 9883 | 1 |
| Hahn1 2 | 6474 | 37.17 | 345.4 | 1 | 1 | 1 | 25.87 | 1.001e+04 | 1 |
| MGH17 1 | 1.271e+07 | 1.271e+07 | 1.271e+07 | nan | 1 | 5.207e+07 | 1.761e+07 | 1.271e+07 | 6.607e+15 |
| MGH17 2 | 604 | 33.64 | 30.24 | 3.75e+13 | 1.016 | 1 | 1523 | 657.6 | 1.017 |
| Lanczos1 1 | 1.049e+18 | 5.459e+16 | 5.507e+16 | 285.4 | 1 | 5.136 | 1.082e+17 | 9.626e+17 | 2.374e+09 |
| Lanczos1 2 | 1.818e+17 | 5.367e+16 | 5.221e+16 | 1 | 1 | 213.2 | 5.065e+15 | 1.625e+17 | 2.606e+06 |
| Lanczos2 1 | 1.364e+09 | 7.103e+07 | 7.166e+07 | 1 | 1 | 1 | 1.446e+08 | 1.081e+09 | 1 |
| Lanczos2 2 | 1.295e+08 | 3.823e+07 | 3.719e+07 | 1 | 1 | 1 | 3.506e+06 | 1.155e+08 | 1 |
| Gauss3 1 | 15.22 | 15.19 | 15.19 | 1 | 1 | 1 | 1 | 15.22 | 1 |
| Gauss3 2 | 3.172 | 2.023 | 2.573 | 8.2 | 1 | 1 | 1.001 | 9.047 | 1 |
| Misra1c 1 | 121.4 | 121.1 | 121.1 | nan | 1 | 1 | 1 | 121.1 | 1 |
| Misra1c 2 | 6.516 | 6.517 | 6.517 | 1 | 1 | 1 | 1 | 6.518 | 1 |
| Misra1d 1 | 20.25 | 20.63 | 20.63 | 1.001 | 1.001 | 1.001 | 1 | 20.63 | 1.001 |
| Misra1d 2 | 2.008 | 2.002 | 2.002 | 1 | 1 | 1 | 1.001 | 2.001 | 1 |
| ENSO 1 | 1.315 | 1.026 | 1.067 | 1.526 | 1.003 | 1.526 | 1 | 1.081 | 1.001 |
| ENSO 2 | 1.06 | 1.025 | 1.025 | 1.084 | 1.002 | 1.084 | 1.065 | 1.061 | 1 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| MGH09 1 | 18.15 | 52.96 | 52.96 | 338.1 | 3.947 | 1 | 7.13 | 46.53 | 3.948 |
| MGH09 2 | 1.807 | 1.181 | 1 | 4.196 | 1.063 | 1.063 | 1.182 | 1.718 | 1.063 |
| Thurber 1 | 1.359 | 1.49 | 1 | 18.14 | 6.775 | 6.787 | 5.655 | 1.946 | 6.77 |
| Thurber 2 | 2.689 | 1.419 | 1.446 | 1 | 1.001 | 1.003 | 2.293 | 2.572 | 1.001 |
| BoxBOD 1 | 2.968 | 2.968 | 2.968 | nan | 2.968 | 2.968 | 2.968 | 1 | 2.968 |
| BoxBOD 2 | 22.91 | 8.641 | 8.641 | 1 | 1 | 1 | 8.641 | 8.382 | 1 |
| Rat42 1 | 152.7 | 15.17 | 15.24 | 1 | 1 | 1 | 14.83 | 207.2 | 1 |
| Rat42 2 | 1.301 | 1.289 | 1.044 | 1 | 1 | 1 | 1.448 | 1.422 | 1 |
| MGH10 1 | 6.234e+05 | 6.282e+05 | 6.215e+05 | 9.056e+49 | 1 | 5.269e+05 | 6.462e+05 | 6.282e+05 | 6.097e+05 |
| MGH10 2 | 8.218e+04 | 1338 | 1335 | nan | 3.105 | 147.2 | 8.409e+04 | 8.091e+04 | 1 |
| Eckerle4 1 | 478 | 490.5 | 490.5 | 478 | 1 | 1 | 478 | 490.5 | 340.7 |
| Eckerle4 2 | 30.92 | 33.83 | 33.83 | 1 | 1 | 1 | 1.001 | 33.83 | 1 |
| Rat43 1 | 251.4 | 178.7 | 83.69 | nan | 1 | 2.938 | 1 | 242.9 | 1 |
| Rat43 2 | 1.071 | 1.006 | 1.006 | 1.01 | 1.01 | 1.01 | 1.01 | 1 | 1.01 |
| Bennett5 1 | 1334 | 566.4 | 1.028 | nan | 1 | 1 | 1819 | 1318 | 1 |
| Bennett5 2 | 713.7 | 6.524 | 2.247 | 1 | 1 | 1.062 | 1571 | 705 | 1 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| PALMER6C | 2.874 | 1 | 2.322 | 1.063e+04 | 9.331 | 1.063e+04 | 2.904 | 3.739 | nan |
| PALMER7C | 66.85 | 14.78 | 14.85 | 4.319e+05 | 2.624 | 4.319e+05 | 74.53 | 111.7 | 1 |
| PALMER8C | 196.8 | 18.62 | 23.16 | 3.051e+05 | 2.304 | 3.051e+05 | 23.38 | 268.5 | 1 |
| YFITU | 4.743e+14 | 1.18e+14 | 6.325e+13 | 1.032 | 1.032 | 1.032 | 2.848e+14 | 3.346e+14 | 1 |
| VESUVIOLS | 1.614 | 1.608 | 1.608 | 5.156e+33 | 1 | 1.403 | 5.241 | 1.608 | 1 |
| DMN15102LS | 6.216 | 5.426 | 3.84 | 8.583 | 8.351 | 1 | 3.745 | 4.341 | 5.634 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| ENGINX 193749 calibration, spectrum 651, peak 19 | 1 | 1.015 | 1.058 | nan | 1.143 | 1.064 | 1.168 | 1.381 | 1.139 |
| ENGINX 193749 calibration, spectrum 651, peak 20 | 1.813 | 1.735 | 1.725 | nan | 1 | 1.808 | 1.216 | 6.084 | 1.001 |
| ENGINX 193749 calibration, spectrum 651, peak 23 | 3.102 | 2.989 | 2.923 | nan | 1 | 3.267 | 2.864 | 21.55 | 3.245 |
| ENGINX 193749 calibration, spectrum 651, peak 5 | 1.057 | 1.077 | 1.077 | nan | 1.137 | 1.222 | 1.353 | 1 | 1.145 |
| ENGINX 193749 calibration, spectrum 651, peak 6 | 1.136 | 1.021 | 1.141 | nan | 1.016 | 1.051 | 1 | 1.132 | 1.016 |
| ENGINX 236516 vanadium, bank 1, 10 brk | 1 | 1 | 1 | 1.138 | 1 | 1.138 | 1.038 | 1.02 | 1 |
| ENGINX 236516 vanadium, bank 1, 30 brk | 1 | 1 | 1 | 1.138 | 1 | 1.138 | 1.113 | 1.03 | 1 |
| EVS14188-90_processed Gaussian peaks 1 | 1.914 | 1.566 | 1.277 | 2.228 | 1.649 | 1.003 | 2.301 | 2.305 | 1 |
| EVS14188-90_processed Gaussian peaks 1 | 1.538 | 1.538 | 1.538 | 1 | 1.053 | 1 | 2.337 | 2.344 | 1 |
| GEM 13 IC peaks | 17.09 | 3.571 | 14.59 | nan | 1 | 1.018 | 8.178 | 26.04 | 1.003 |
| WISH17701 tube 3 calibration, peak 1 | 1.005 | 5.036 | 5.081 | 1 | 13.44 | 1 | 5.281 | 7.485 | 1 |
| WISH17701 tube 3 calibration, peak 2 | 1 | 1.267 | 1.189 | 1 | 1 | 1 | 1.511 | 3.546 | 1 |
| WISH17701 tube 3 calibration, peak 3 | 2.604 | 10.96 | 9.291 | 1 | 1 | 1 | 11.54 | 21.39 | 1 |
| WISH17701 tube 3 calibration, peak 4 | 16.21 | 16.31 | 17.19 | 1 | 1 | 1 | 18.63 | 36.03 | 1 |
| WISH17701 tube 3 calibration, peak 5 | 1.667 | 1.871 | 1.643 | 1 | 1 | 1 | 2.334 | 3.402 | 1 |
| WISH17701 tube 3 calibration, peak 6 | 3.922 | 3.822 | 3.923 | 1 | 1 | 1 | 5.876 | 16.78 | 1 |
| WISH17701 tube 3 calibration, peak 7 | 4.736 | 1.344 | 4.82 | 2.948e+06 | 1 | 1 | 5.245 | 6.1 | 1 |
| WISH17701 tube 3 calibration, peak 8 | 2.154 | 2.198 | 1.992 | 1 | 1 | 1 | 2.799 | 3.845 | 1 |
| WISH17701 tube 3 calibration, peak 9 | 1.133 | 1.132 | 1.28 | 1 | 1 | 1 | 1.283 | 1.594 | 1 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| NIST, “lower” difficulty | 1.917 | 1.763 | 1.31 | 1.035 | 1.065 | 1.047 | 1.466 | 8.084 | 1.214 |
| NIST, “average” difficulty | 2.376 | 2.513 | 3.014 | 1.018 | 1.256 | 1.075 | 2.117 | 9.286 | 1.718 |
| NIST, “higher” difficulty | 1.193 | 1.453 | 2.154 | 1.093 | 1.148 | 1.765 | 1.16 | 3.619 | 1.323 |
| CUTEst | 3.255 | 18.66 | 13.39 | 1.318 | 1.829 | 1 | 1.695 | 16.48 | 12.33 |
| Neutron data | 3.545 | 5.796 | 5.746 | 1 | 1.099 | 1.077 | 1.715 | 4.205 | 2.495 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| Misra1a 1 | 3.628 | 1.143 | 1 | 1.005 | 1.146 | 1.018 | 1.428 | 1.924 | 1.15 |
| Misra1a 2 | 1 | 1.525 | 1.051 | 1.054 | 1.049 | 1.058 | 1.288 | 2.419 | 1.189 |
| Chwirut2 1 | 3.623 | 13.04 | 12.65 | 1 | 2.051 | 1.09 | 1.272 | 7.138 | 2.322 |
| Chwirut2 2 | 1.247 | 4.151 | 14.19 | 1 | 1.067 | 1.011 | 1.405 | 7.675 | 1.166 |
| Chwirut1 1 | 2.651 | 30.15 | 28.61 | 1 | 1.322 | 1.045 | 1.189 | 13.2 | 18.16 |
| Chwirut1 2 | 1.413 | 41.07 | 36.49 | 1.029 | 1 | 1.018 | 1.453 | 17.24 | 1.236 |
| Lanczos3 1 | 3.605 | 3.162 | 2.54 | 1.048 | 2.752 | 1 | 2.125 | 8.493 | 2.576 |
| Lanczos3 2 | 1.338 | 2.545 | 3.203 | 1 | 1.061 | 5.59 | 3.318 | 9.571 | 1.18 |
| Gauss1 1 | 1.521 | 1 | 1.15 | 1.283 | 1.518 | 1.517 | 6.998 | 61.43 | 70.51 |
| Gauss1 2 | 1.263 | 19.64 | 56.44 | 1.161 | 1.022 | 1 | 5.12 | 45.89 | 52.21 |
| Gauss2 1 | 3.714 | 1 | 1.018 | 1.294 | 1.323 | 1.548 | 6.346 | 57.34 | 66.04 |
| Gauss2 2 | 2.313 | 1 | 1.256 | 1.225 | 1.404 | 1.4 | 9.05 | 60.21 | 69.86 |
| DanWood 1 | 3.447 | 2 | 1.365 | 1.041 | 1 | 1.049 | 1.113 | 3.466 | 1.079 |
| DanWood 2 | 1 | 1.18 | 1.22 | 1.013 | 1.015 | 1.058 | 1.547 | 3.745 | 1.072 |
| Misra1b 1 | 3.045 | 1.101 | 1.081 | 1 | 1.064 | 1.005 | 1.48 | 1.622 | 1.193 |
| Misra1b 2 | 1.038 | 1.061 | 1.14 | 1.616 | 1.031 | 1 | 1.394 | 2.065 | 1.119 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| Kirby2 1 | 2.466 | 27.66 | 28.18 | 1.089 | 1.087 | 1 | 2.104 | 15.74 | 2.708 |
| Kirby2 2 | 1.496 | 28.78 | 28.33 | 1 | 1.18 | 1.092 | 2.112 | 18.05 | 2.242 |
| Hahn1 1 | 2.338 | 1.79 | 37.52 | 17.6 | 23.66 | 1.1 | 1.575 | 20.91 | 1 |
| Hahn1 2 | 1.074 | 46.11 | 25.85 | 1.015 | 1.106 | 1 | 2.759 | 24.71 | 1.352 |
| MGH17 1 | 2.492 | 1.035 | 1 | 1.31 | 8.089 | 2.115 | 1.125 | 2.459 | 1.491 |
| MGH17 2 | 1.427 | 1.768 | 2.957 | 1 | 7.974 | 5.232 | 1.128 | 7.163 | 9.131 |
| Lanczos1 1 | 2.841 | 3.231 | 2.486 | 1.006 | 2.584 | 1 | 2.122 | 8.269 | 1.944 |
| Lanczos1 2 | 1.234 | 2.577 | 3.071 | 1 | 1.024 | 4.233 | 2.784 | 9.353 | 1.008 |
| Lanczos2 1 | 3.627 | 3.309 | 2.695 | 1 | 2.763 | 1.05 | 2.346 | 8.758 | 2.182 |
| Lanczos2 2 | 1.265 | 2.449 | 3.131 | 1.021 | 1.089 | 4.293 | 3.322 | 9.219 | 1 |
| Gauss3 1 | 2.414 | 1 | 1.077 | 1.695 | 1.785 | 1.786 | 10.87 | 62.85 | 72.52 |
| Gauss3 2 | 1.487 | 36.57 | 15.59 | 4.071 | 1.331 | 1 | 6.78 | 39.31 | 45.25 |
| Misra1c 1 | 3.008 | 1.068 | 1.009 | 1.279 | 1 | 1.058 | 1.282 | 2.089 | 1.168 |
| Misra1c 2 | 1.069 | 1.157 | 1.043 | 1.451 | 1.036 | 1 | 1.257 | 2.124 | 1.378 |
| Misra1d 1 | 3.784 | 1.249 | 1.146 | 1 | 1.139 | 1.099 | 1.761 | 2.127 | 1.329 |
| Misra1d 2 | 1 | 1.067 | 1.088 | 1.039 | 1.046 | 1.017 | 1.301 | 1.549 | 1.091 |
| ENSO 1 | 3.544 | 115.8 | 74.75 | 1 | 108 | 1.386 | 16.06 | 87.49 | 107.7 |
| ENSO 2 | 3.77 | 98.17 | 147.5 | 1 | 104.3 | 1.03 | 12.13 | 82.23 | 106.9 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| MGH09 1 | 5.288 | 1 | 1.078 | 1.698 | 1.34 | 2.401 | 2.913 | 1.775 | 2.08 |
| MGH09 2 | 1.03 | 1.334 | 1.512 | 1.47 | 1.09 | 1.07 | 1 | 3.695 | 1.1 |
| Thurber 1 | 1.006 | 7.124 | 7.251 | 10.08 | 3.972 | 2.645 | 1 | 3.85 | 4.471 |
| Thurber 2 | 1 | 6.238 | 15.17 | 25.36 | 9.846 | 6.471 | 1.664 | 9.338 | 11.1 |
| BoxBOD 1 | 2.342 | 1.056 | 1.052 | 1.218 | 1.008 | 1 | 1.125 | 3.096 | 1.161 |
| BoxBOD 2 | 1.045 | 1.073 | 1.098 | 1.063 | 1.618 | 1.073 | 1.056 | 3.153 | 1 |
| Rat42 1 | 3.149 | 1.34 | 1.245 | 1.022 | 1.052 | 1 | 1.265 | 3.512 | 1.057 |
| Rat42 2 | 1.116 | 4.528 | 5.022 | 1 | 1.056 | 1.001 | 1.166 | 3.542 | 6.594 |
| MGH10 1 | 5.74 | 1 | 3.761 | 1.141 | 4.286 | 3.409 | 1.155 | 2.312 | 5.005 |
| MGH10 2 | 1 | 3.895 | 5.263 | 1.362 | 4.603 | 4.039 | 1.021 | 3.807 | 4.765 |
| Eckerle4 1 | 3.128 | 1.022 | 1.18 | 1 | 1.156 | 3.707 | 1.089 | 1.467 | 1.193 |
| Eckerle4 2 | 1.051 | 1.085 | 1.08 | 1 | 1.206 | 1.085 | 1.197 | 1.078 | 1.17 |
| Rat43 1 | 2.505 | 1.566 | 1.581 | 1.123 | 1.046 | 1 | 2.815 | 4.697 | 1.453 |
| Rat43 2 | 1 | 7.314 | 5.865 | 1.037 | 1.022 | 1.129 | 1.712 | 5.968 | 1.046 |
| Bennett5 1 | 2.741 | 29.52 | 2.727 | 1.004 | 1 | 10.99 | 1.072 | 9.937 | 1.599 |
| Bennett5 2 | 1.27 | 24.75 | 2.849 | 1 | 1.139 | 11.25 | 1.218 | 9.038 | 1.177 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| PALMER6C | 3.203 | 37.49 | 14.98 | 1.107 | 2.015 | 1 | 1.682 | 16.59 | 3.542 |
| PALMER7C | 3.71 | 28.69 | 34.96 | 1.047 | 19.52 | 1 | 1.708 | 17.97 | 27.65 |
| PALMER8C | 3.308 | 31.74 | 34.65 | 1.529 | 17.39 | 1 | 4.452 | 16.36 | 25.99 |
| YFITU | 3.193 | 8.638 | 9.006 | 1.582 | 1.049 | 1 | 1.077 | 4.637 | 1.186 |
| VESUVIOLS | 1.209 | 7.944 | 11.8 | 1.612 | 1.603 | 1.14 | 1 | 41.34 | 1.609 |
| DMN15102LS | 5.209 | 5.145 | 5.854 | 1 | 1.644 | 3.548 | 2.691 | 8.067 | 21.12 |
| BFGS | Conjugate gradient (Fletcher-Reeves imp.) | Conjugate gradient (Polak-Ribiere imp.) | Damping | Levenberg-Marquardt | Levenberg-MarquardtMD | Simplex | SteepestDescent | Trust Region | |
|---|---|---|---|---|---|---|---|---|---|
| ENGINX 193749 calibration, spectrum 651, peak 19 | 1.245 | 3.983 | 2.818 | 1 | 2.72 | 1.285 | 3.901 | 14.78 | 17.93 |
| ENGINX 193749 calibration, spectrum 651, peak 20 | 1.674 | 8.281 | 4.713 | 1 | 4.067 | 1.361 | 3.286 | 17.37 | 21.73 |
| ENGINX 193749 calibration, spectrum 651, peak 23 | 1.359 | 2.566 | 2.889 | 1.032 | 1.542 | 1 | 1.297 | 14.64 | 19.83 |
| ENGINX 193749 calibration, spectrum 651, peak 5 | 1.118 | 4.324 | 1.408 | 1 | 1.099 | 1.175 | 4.255 | 6.036 | 2.991 |
| ENGINX 193749 calibration, spectrum 651, peak 6 | 1 | 2.992 | 1.967 | 1.108 | 2.317 | 1.125 | 3.347 | 5.617 | 30.43 |
| ENGINX 236516 vanadium, bank 1, 10 brk | 19.23 | 24.26 | 25.23 | 1.069 | 5.64 | 1 | 17.53 | 190.6 | 2.93 |
| ENGINX 236516 vanadium, bank 1, 30 brk | 32.84 | 101 | 135.2 | 1 | 6.909 | 1.004 | 7.944 | 175 | 2.661 |
| EVS14188-90_processed Gaussian peaks 1 | 83.93 | 39.91 | 40.09 | 1 | 2.115 | 3.198 | 1.162 | 25.14 | 3.585 |
| EVS14188-90_processed Gaussian peaks 1 | 17.25 | 35.46 | 36.52 | 2.102 | 1 | 1.913 | 1.018 | 21.93 | 2.495 |
| GEM 13 IC peaks | 1.354 | 41.38 | 44.17 | 1 | 4.599 | 3.344 | 10.27 | 3.188 | 10.59 |
| WISH17701 tube 3 calibration, peak 1 | 7.068 | 5.796 | 5.604 | 1.103 | 1 | 1.076 | 1.895 | 4.189 | 1.268 |
| WISH17701 tube 3 calibration, peak 2 | 5.019 | 5.489 | 5.62 | 1.011 | 1 | 1.276 | 1.767 | 4.071 | 1.276 |
| WISH17701 tube 3 calibration, peak 3 | 9.898 | 6.215 | 6.334 | 1.818 | 1.096 | 1 | 1.715 | 4.205 | 1.191 |
| WISH17701 tube 3 calibration, peak 4 | 3.493 | 5.53 | 5.487 | 1 | 1.072 | 1.01 | 1.426 | 3.866 | 1.154 |
| WISH17701 tube 3 calibration, peak 5 | 9.501 | 5.589 | 6.026 | 1.063 | 1 | 1.052 | 1.446 | 4.002 | 1.185 |
| WISH17701 tube 3 calibration, peak 6 | 3.091 | 5.472 | 5.569 | 1 | 1.137 | 1.077 | 1.391 | 3.901 | 1.106 |
| WISH17701 tube 3 calibration, peak 7 | 3.545 | 6.025 | 5.746 | 1 | 1.037 | 1.092 | 1.5 | 4.034 | 1.274 |
| WISH17701 tube 3 calibration, peak 8 | 4.326 | 5.938 | 5.948 | 1 | 1.014 | 1.068 | 1.43 | 4.077 | 1.313 |
| WISH17701 tube 3 calibration, peak 9 | 3.089 | 5.646 | 5.913 | 1.083 | 1.075 | 1 | 1.384 | 4.042 | 1.253 |
Category: Concepts