Table 1 Numerical comparisons of four CG methods
From: Least-squares-based three-term conjugate gradient methods
Problems | LSTT+ | MLSTT+ | TTPRP | TTHS |
|---|---|---|---|---|
Name/n | Itr/NF/NG/Tcpu/\(\|g_{*}\|\) | Itr/NF/NG/Tcpu/\(\|g_{*}\| \) | Itr/NF/NG/Tcpu/\(\|g_{*}\|\) | Itr/NF/NG/Tcpu/\(\|g_{*}\|\) |
bdexp 1000 | 3/2/3/0.023/2.19e-108 | 3/2/3/0.002/2.19e-108 | 3/2/3/0.009/3.49e-107 | 3/2/3/0.002/3.45e-107 |
bdexp 5000 | 3/2/3/0.010/9.67e-110 | 3/2/3/0.009/9.67e-110 | 3/2/3/0.009/1.71e-109 | 3/2/3/0.009/1.71e-109 |
nnbdexp 10,000 | 3/2/3/0.017/8.32e-110 | 3/2/3/0.017/8.32e-110 | 3/2/3/0.017/1.11e-109 | 3/2/3/0.017/1.11e-109 |
exdenschnf 3000 | 29/81/30/0.054/3.80e-07 | 26/78/26/0.050/3.42e-07 | 31/85/34/0.057/1.15e-07 | 32/77/32/0.054/9.47e-07 |
exdenschnf 4000 | 24/79/25/0.063/1.94e-07 | 26/78/26/0.066/7.04e-07 | 31/85/34/0.075/1.37e-07 | 34/79/34/0.074/4.84e-07 |
exdenschnf 5000 | 27/81/28/0.084/2.46e-07 | 27/79/27/0.084/1.96e-07 | 31/85/34/0.092/1.51e-07 | 34/78/34/0.091/6.05e-07 |
exdenschnb 1000 | 26/54/27/0.008/2.81e-07 | 21/57/22/0.007/9.70e-08 | 39/58/40/0.010/4.23e-07 | 20/58/21/0.007/8.90e-07 |
exdenschnb 2000 | 26/54/27/0.013/3.72e-07 | 21/57/22/0.012/1.36e-07 | 39/58/40/0.018/6.02e-07 | 21/59/22/0.012/5.34e-07 |
himmelbg 10,000 | 3/6/7/0.016/3.75e-28 | 3/6/7/0.016/3.75e-28 | 3/6/7/0.015/4.90e-28 | 3/6/7/0.015/4.89e-28 |
himmelbg 20,000 | 3/6/7/0.030/5.30e-28 | 3/6/7/0.030/5.30e-28 | 3/6/7/0.030/6.93e-28 | 3/6/7/0.030/6.92e-28 |
himmelbg 25,000 | 3/6/7/0.038/5.92e-28 | 3/6/7/0.038/5.92e-28 | 3/6/7/0.037/7.75e-28 | 3/6/7/0.037/7.74e-28 |
genquartic 100,000 | 43/85/53/1.049/2.95e-07 | 29/64/29/0.741/5.84e-07 | 64/118/91/1.564/8.98e-07 | 55/121/82/1.440/2.75e-07 |
genquartic 1,000,000 | 45/94/57/12.877/6.87e-07 | 39/87/49/11.799/5.47e-07 | 76/162/122/22.901/6.28e-07 | 57/112/79/16.166/9.91e-07 |
genquartic 5,000,000 | 44/96/57/65.600/3.38e-07 | 45/84/51/62.282/3.12e-08 | 81/185/138/126.781/1.50e-07 | 42/109/61/67.433/4.05e-07 |
biggsb1 200 | 802/376/967/0.077/9.19e-07 | 671/349/823/0.065/6.83e-07 | 1105/827/1496/0.108/9.02e-07 | 729/328/871/0.065/8.56e-07 |
biggsb1 400 | 1726/877/2143/0.203/9.01e-07 | 1632/841/2031/0.201/8.39e-07 | 1992/1465/2703/0.246/8.02e-07 | NaN/NaN/NaN/NaN/4.04e-06 |
sine 30,000 | 39/59/41/0.556/7.11e-07 | 130/158/182/1.663/1.37e-07 | 971/1607/1748/12.793/4.81e-07 | 304/328/439/3.544/4.74e-07 |
sine 50,000 | 41/109/70/1.359/8.18e-07 | 131/187/196/2.916/5.26e-07 | NaN/NaN/NaN/NaN/2.87e-05 | 363/484/577/7.323/9.63e-07 |
sine 200,000 | 189/316/320/17.825/1.92e-07 | 114/164/168/11.351/4.66e-07 | NaN/NaN/NaN/NaN/5.36e-05 | 1227/1636/2017/104.296/6.06e-07 |
sinquad 3 | 38/67/51/0.004/9.88e-07 | 60/116/94/0.006/1.91e-07 | 77/193/153/0.008/3.34e-07 | 65/81/82/0.005/8.11e-07 |
fletcbv3 50 | 97/113/152/0.011/2.19e-07 | 139/172/219/0.016/6.63e-07 | 159/185/250/0.019/2.37e-07 | 134/164/211/0.016/1.49e-07 |
fletcbv3 100 | 490/414/684/0.099/3.17e-07 | 899/612/1181/0.175/3.45e-07 | 348/367/517/0.074/4.28e-07 | NaN/NaN/NaN/NaN/7.69e-04 |
eg2 20 | 32/88/49/0.004/9.14e-07 | 51/119/82/0.006/5.52e-07 | 62/247/157/0.009/9.50e-07 | 96/280/209/0.012/7.86e-07 |
nonscomp 20,000 | 79/110/96/0.298/6.66e-07 | 61/89/68/0.239/7.68e-07 | 140/153/178/0.492/8.47e-07 | 142/142/175/0.484/6.22e-07 |
nonscomp 30,000 | 55/93/64/0.325/7.66e-07 | 66/83/70/0.361/9.01e-07 | 81/123/105/0.470/7.86e-07 | 149/141/181/0.742/8.09e-07 |
nonscomp 50,000 | 66/86/70/0.585/5.09e-07 | 61/91/69/0.601/7.01e-07 | 89/121/110/0.822/7.51e-07 | 77/107/92/0.708/4.46e-07 |
cosine 5000 | 39/72/49/0.093/9.27e-07 | 23/59/26/0.060/3.61e-07 | 90/158/142/0.227/9.66e-07 | 57/89/75/0.121/3.61e-07 |
cosine 10,000 | 28/60/31/0.131/2.38e-07 | 21/62/25/0.115/7.31e-07 | 517/1054/1002/2.277/6.53e-07 | 61/93/81/0.236/9.26e-07 |
cosine 1,000,000 | 145/277/257/72.095/8.55e-09 | 22/59/24/13.451/8.68e-07 | NaN/NaN/NaN/NaN/3.07e-04 | 277/393/447/119.491/5.17e-07 |
dixmaana 3000 | 25/64/26/0.207/2.49e-07 | 16/64/17/0.174/3.25e-07 | 20/63/21/0.186/1.56e-07 | 18/65/19/0.183/1.49e-07 |
dixmaand 3000 | 17/63/17/0.177/5.34e-07 | 13/57/13/0.149/8.63e-07 | 17/65/17/0.179/9.00e-07 | 20/66/20/0.191/2.94e-07 |
dixmaane 3000 | 357/227/440/1.805/7.00e-07 | 374/252/469/1.939/4.33e-07 | 264/231/349/1.472/7.23e-07 | 436/305/557/2.279/9.23e-07 |
dixmaang 3000 | 296/210/369/1.541/6.80e-07 | 344/217/420/1.741/5.51e-07 | 326/249/418/1.741/8.47e-07 | 327/164/377/1.543/9.26e-07 |
dixmaanj 3000 | 972/551/1217/4.699/9.58e-07 | 1131/542/1372/5.284/9.09e-07 | 960/715/1286/5.035/8.43e-07 | 1250/597/1518/5.800/9.04e-07 |
dixmaanl 3000 | 983/544/1222/4.736/8.17e-07 | NaN/NaN/NaN/NaN/8.19e-06 | NaN/NaN/NaN/NaN/1.73e-05 | NaN/NaN/NaN/NaN/1.46e-05 |