From: A quasi-Newton algorithm for large-scale nonlinear equations
 |  | New method with CG | Normal method (only main algorithm) | ||||||
---|---|---|---|---|---|---|---|---|---|
P | Dim | NI/NG | GF | GD | cpu time | NI/NG | GF | GD | cpu time |
1 | 1000 | 1/1 | 6.676674e−006 | 1.335335e−005 | 0.000000e+000 | 0/2 | 6.676674e−006 | 1.335335e−005 | 0.000000e+000 |
2000 | 1/1 | 3.335834e−006 | 6.671668e−006 | 0.000000e+000 | 0/2 | 3.335834e−006 | 6.671668e−006 | 0.000000e+000 | |
3000 | 1/1 | 2.223334e−006 | 4.446667e−006 | 1.560010e−002 | 0/2 | 2.223334e−006 | 4.446667e−006 | 3.120020e−002 | |
2 | 1000 | 12/17 | 1.570352e−007 | 1.214954e−007 | 1.544410e+000 | 199/2879 | 1.624268e−004 | 1.228551e+000 | 1.338801e+002 |
2000 | 200/2927 | 8.144022e−005 | 3.138945e−001 | 8.647135e+002 | 199/2928 | 8.144022e−005 | 3.138945e−001 | 8.680832e+002 | |
3000 | 200/2326 | 5.434381e−005 | 2.481121e−003 | 1.614626e+003 | 199/2327 | 5.434381e−005 | 2.481121e−003 | 1.622785e+003 | |
3 | 1000 | 8/8 | 4.194859e−006 | 8.389718e−006 | 1.560010e−002 | 115/1009 | 5.838535e−008 | 1.171251e−007 | 7.996611e+001 |
2000 | 8/8 | 7.775106e−006 | 1.555021e−005 | 7.800050e−002 | 117/1040 | 1.161670e−007 | 2.328056e−007 | 5.662368e+002 | |
3000 | 9/9 | 1.614597e−012 | 3.231630e−012 | 1.553770e+001 | 137/1362 | 1.739498e−007 | 3.484891e−007 | 2.141410e+003 | |
4 | 1000 | 92/165 | 5.632576e−006 | 5.669442e−006 | 2.215214e+000 | 199/285 | 3.703283e+001 | 1.196051e+001 | 1.356897e+002 |
2000 | 87/156 | 6.245922e−006 | 6.085043e−006 | 1.502290e+001 | 199/230 | 3.637504e+000 | 9.570779e+000 | 9.591097e+002 | |
3000 | 94/169 | 6.678153e−006 | 6.437585e−006 | 4.731510e+001 | 199/234 | 2.639260e+002 | 1.904865e+001 | 3.096277e+003 | |
5 | 1000 | 22/51 | 8.288299e−006 | 6.268946e−007 | 2.106014e+000 | 199/2570 | 3.195300e+004 | 4.649782e+006 | 1.779971e+001 |
2000 | 21/50 | 4.114462e−006 | 1.943351e−006 | 5.179233e+000 | 199/2652 | 6.395300e+004 | 1.354972e+005 | 8.327333e+001 | |
3000 | 21/51 | 9.843373e−006 | 8.504719e−006 | 1.597450e+001 | 199/2853 | 9.595300e+004 | 1.135356e+005 | 1.314776e+002 | |
6 | 1000 | 9/11 | 5.984185e−012 | 1.197596e−011 | 7.176046e−001 | 6/9 | 6.069722e−007 | 1.118437e−006 | 4.149627e+000 |
2000 | 9/11 | 1.505191e−006 | 3.010383e−006 | 7.800050e−002 | 6/9 | 1.210931e−006 | 2.231765e−006 | 2.898499e+001 | |
3000 | 9/11 | 2.251571e−006 | 4.503142e−006 | 1.404009e−001 | 6/9 | 1.814891e−006 | 3.345093e−006 | 9.300780e+001 | |
7 | 1000 | 200/602 | 1.208240e−003 | 4.697005e+000 | 3.424222e+001 | 199/573 | 3.156137e+005 | 3.893380e+004 | 1.378113e+002 |
2000 | 200/760 | 1.612671e+001 | 9.034319e+000 | 2.420200e+002 | 199/644 | 1.014481e+006 | 3.131576e+005 | 9.872367e+002 | |
3000 | 200/693 | 5.570227e−003 | 9.501149e+001 | 7.698181e+002 | 199/743 | 9.357473e+007 | 2.087488e+007 | 3.087119e+003 | |
8 | 1000 | 2/2 | 0.000000e+000 | 0.000000e+000 | 0.000000e+000 | 1/3 | 0.000000e+000 | 0.000000e+000 | 6.552042e−001 |
2000 | 2/2 | 0.000000e+000 | 0.000000e+000 | 0.000000e+000 | 1/3 | 0.000000e+000 | 0.000000e+000 | 4.820431e+000 | |
3000 | 2/2 | 0.000000e+000 | 0.000000e+000 | 6.240040e−002 | 1/3 | 0.000000e+000 | 0.000000e+000 | 1.538170e+001 | |
9 | 1000 | 67/118 | 7.138941e−006 | 1.820053e−005 | 3.010819e+000 | 2/5 | 2.358640e−006 | 4.611203e−006 | 1.404009e+000 |
2000 | 70/124 | 6.342724e−006 | 1.607326e−005 | 2.062333e+001 | 2/5 | 5.917002e−007 | 1.169969e−006 | 9.703262e+000 | |
3000 | 74/131 | 7.447187e−006 | 1.799920e−005 | 6.450641e+001 | 2/5 | 2.632811e−007 | 5.225655e−007 | 3.084140e+001 | |
10 | 1000 | 26/49 | 2.044717e−008 | 3.900140e−008 | 2.359983e+002 | 121/125 | 7.382123e−006 | 1.467673e−005 | 4.987196e+002 |
2000 | 24/47 | 9.030382e−006 | 2.717060e−006 | 1.847286e+003 | 121/125 | 7.454090e−006 | 1.481981e−005 | 3.852538e+003 | |
3000 | 27/51 | 6.468831e−009 | 1.138377e−008 | 6.632227e+003 | 121/125 | 7.523322e−006 | 1.495745e−005 | 1.299774e+004 |