一个带重启步的改进PRP型谱共轭梯度法
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江羡珍,廖伟,简金宝,毋晓迪
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An Improved PRP Type Spectral Conjugate Gradient Method with Restart Steps
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Xianzhen Jiang,Wei Liao,Jinbao Jian,Xiaodi Wu
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表 1 数值试验报告
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| Problems | JLJW+ | KD | DK | HZ | SPF2 | | Name/n | Itr/Tcpu/||g*|| | Itr/Tcpu/||g*|| | Itr/Tcpu/||g*|| | Itr/Tcpu/||g*|| | Itr/Tcpu/||g*|| | | bard 3 | 1430/4.93/7.6e-07 | 1565/5.19/8.0e-07 | F/F/3.2e-05 | 620/2.00/4.0e-07 | 235/0.64/6.6e-07 | | beale 2 | 631/0.96/3.6e-07 | 326/0.52/7.7e-07 | 86/0.11/1.6e-07 | 251/0.37/6.2e-07 | 142/0.20/4.3e-07 | | box 3 | 150/0.26/2.1e-07 | 330/0.57/6.0e-07 | 134/0.26/1.4e-08 | 475/0.89/8.9e-07 | 91/0.13/5.2e-07 | | cosine 300 | 19/0.03/5.2e-07 | 26/0.09/3.3e-07 | F/F/1.2e-04 | 32/0.06/4.9e-08 | F/F/3.0e+02 | | cosine 1500 | 1560/11.26/1.5e-07 | F/F/1.4e+03 | F/F/2.8e+03 | F/F/1.2e+02 | F/F/1.8e+03 | | cosine 4500 | F/F/2.9e+02 | F/F/5.8e-04 | F/F/1.2e+04 | 477/11.19/2.9e-07 | F/F/2.1e+03 | | dixmaana 3000 | 18/0.99/3.4e-07 | 17/0.90/3.1e-07 | 23/1.22/6.0e-07 | 26/1.75/1.3e-07 | 24/1.38/1.9e-07 | | dixmaana 12000 | 18/3.14/6.8e-07 | 17/2.93/6.2e-07 | 25/4.16/1.1e-07 | 21/3.70/1.6e-07 | 24/4.05/3.7e-07 | | dixmaanb 3000 | 11/0.39/7.4e-07 | 12/0.50/3.3e-07 | 34/1.76/1.7e-07 | 49/3.92/9.6e-08 | 14/0.61/1.5e-07 | | dixmaanb 12000 | 11/1.17/4.4e-07 | 12/1.51/5.8e-07 | 47/10.10/9.0e-08 | 40/10.30/6.5e-07 | 13/1.55/2.7e-07 | | dixmaanc 3000 | 24/1.48/3.8e-08 | 25/1.54/5.5e-07 | 29/1.62/2.4e-07 | 33/2.20/1.9e-07 | 35/2.18/8.0e-07 | | dixmaanc 12000 | 16/2.37/1.0e-06 | 25/4.38/4.5e-07 | 27/4.39/8.2e-07 | 73/18.86/5.6e-07 | 67/15.50/9.6e-07 | | dixmaand 3000 | 25/1.28/1.3e-07 | 25/1.32/3.6e-07 | 29/1.56/3.3e-07 | 54/4.45/2.3e-07 | 45/2.73/6.7e-07 | | dixmaand 12000 | 22/3.41/5.5e-07 | 23/3.67/6.5e-07 | 44/8.42/7.7e-07 | 29/5.73/7.2e-07 | 50/10.73/2.7e-07 | | dixmaane 6000 | 1308/199.45/9.0e-07 | 1229/192.04/9.3e-07 | 1941/331.01/8.5e-07 | 1716/274.31/9.3e-07 | 564/82.65/7.7e-07 | | dixmaanf 4500 | 775/94.63/8.3e-07 | 1258/161.65/7.9e-07 | 396/53.77/8.5e-07 | 1165/155.96/9.0e-07 | 470/59.77/7.1e-07 | | dixmaanf 9000 | 1080/237.42/9.3e-07 | 1078/246.31/8.8e-07 | 1396/340.53/9.4e-07 | F/F/1.8e-05 | 383/80.92/4.1e-07 | | dixmaang 7500 | 889/168.72/8.8e-07 | 1154/220.67/5.8e-07 | 1239/250.95/8.9e-07 | 1682/327.37/9.0e-07 | 614/112.05/9.5e-07 | | dixmaanh 4500 | 1417/179.40/9.2e-07 | 1324/169.60/9.8e-07 | 1006/137.94/7.2e-07 | 953/120.53/9.9e-07 | 704/81.78/9.8e-07 | | dixmaani 120 | 1930/9.09/8.7e-07 | 1595/7.68/6.7e-07 | F/F/1.2e-03 | F/F/8.4e-07 | 731/3.29/4.2e-07 | | dixmaanj 2700 | 1193/94.28/8.5e-07 | 1382/108.65/6.2e-07 | 1320/110.36/9.5e-07 | F/F/1.0e-05 | 1153/85.27/6.4e-07 | | dixmaank 3000 | 1142/98.31/6.5e-07 | 1158/100.76/7.8e-07 | F/F/4.0e-05 | F/F/2.7e-05 | 1799/154.65/6.6e-07 | | dixmaanl 300 | 1554/14.02/9.8e-07 | 1424/12.64/8.9e-07 | F/F/4.6e-04 | F/F/8.0e-05 | 826/7.12/7.4e-07 | | dixon3dq 50 | 1199/1.50/8.8e-07 | 1613/2.28/6.0e-07 | F/F/5.9e-05 | 1836/2.41/5.3e-07 | 629/0.82/6.0e-07 | | dixon3dq 88 | 1934/2.80/8.3e-07 | 1476/2.09/6.7e-07 | F/F/1.0e-02 | F/F/4.9e-04 | 1227/1.65/5.2e-07 | | dqdrtic 60000 | 496/35.92/7.8e-07 | 426/31.92/2.8e-07 | 197/13.41/4.1e-07 | 917/67.92/7.1e-07 | 312/21.78/6.2e-07 | | dqrtic 100 | 22/0.06/5.7e-07 | 23/0.04/6.4e-07 | 34/0.04/7.7e-07 | 28/0.03/1.8e-07 | 60/0.12/1.8e-07 | | dqrtic 450 | 34/0.13/2.8e-07 | 47/0.19/3.4e-07 | 33/0.15/7.4e-07 | 31/0.13/5.0e-07 | 60/0.36/5.7e-07 | | edensch 10000 | 46/4.59/9.5e-07 | 54/6.25/6.2e-07 | F/F/8.7e-06 | F/F/3.8e-06 | F/F/3.3e-06 | | edensch 50000 | 55/24.21/1.9e-07 | 65/29.17/8.8e-07 | F/F/1.0e-04 | F/F/1.8e-05 | F/F/1.2e-04 | | edensch 100000 | 126/93.46/9.7e-07 | F/F/4.8e-05 | F/F/2.3e-05 | 120/139.38/5.3e-07 | F/F/2.0e-04 | | eg2 30 | F/F/2.9e-06 | F/F/3.0e-01 | 313/0.43/8.0e-07 | F/F/3.2e-03 | F/F/1.1e-05 | | eg2 80 | F/F/2.5e-04 | F/F/5.8e-06 | F/F/4.0e-01 | F/F/2.8e-02 | F/F/1.9e-05 | | engval1 6 | 87/0.11/1.9e-07 | 95/0.14/2.4e-08 | F/F/4.7e-01 | F/F/8.8e-01 | F/F/1.8e-01 | | fletchcr 10000 | 145/3.81/1.3e-07 | F/F/1.1e-03 | F/F/3.1e-04 | F/F/9.5e-04 | F/F/6.9e-04 | | fletchcr 300000 | 211/118.78/3.9e-07 | F/F/9.2e-03 | F/F/6.2e-03 | F/F/9.5e-04 | F/F/2.6e-02 | | freuroth 20 | 1700/2.52/9.8e-07 | 476/0.66/9.2e-07 | F/F/1.5e-05 | 455/0.60/6.8e-07 | F/F/6.8e-05 | | freuroth 36 | F/F/2.2e-06 | F/F/6.3e-06 | F/F/8.2e-06 | F/F/6.5e-05 | F/F/7.5e-05 | | genrose 2000 | 574/2.28/2.8e-07 | 399/1.94/4.1e-07 | 395/1.77/6.1e-07 | 1259/5.68/9.6e-07 | 692/2.85/4.4e-07 | | genrose 47000 | 270/25.44/6.7e-07 | 336/31.54/1.3e-07 | 474/42.83/7.1e-07 | 854/76.03/9.0e-07 | 571/48.69/8.7e-07 | | gulf 3 | 2/0.00/0.0e+00 | 2/0.00/0.0e+00 | 2/0.00/0.0e+00 | 2/0.00/0.0e+00 | 2/0.00/0.0e+00 | | helix 3 | 479/1.02/1.6e-07 | 282/0.62/4.2e-07 | 316/0.60/7.0e-07 | 731/1.56/6.7e-07 | F/F/3.5e+03 | | himmelbg 1000 | 3/0.01/1.6e-28 | 3/0.00/1.3e-28 | 3/0.00/1.6e-28 | 3/0.00/1.2e-28 | 3/0.00/1.6e-28 | | himmelbg 10000 | 3/0.01/5.2e-28 | 3/0.01/4.2e-28 | 3/0.01/5.0e-28 | 3/0.01/3.8e-28 | 3/0.01/5.0e-28 | | himmelbg 100000 | 3/0.10/1.6e-27 | 3/0.11/1.3e-27 | 3/0.12/1.6e-27 | 3/0.11/1.2e-27 | 3/0.12/1.6e-27 | | kowosb 4 | 774/1.40/7.0e-07 | 817/1.55/4.7e-07 | 1574/3.07/8.7e-07 | F/F/5.2e-04 | 239/0.43/7.5e-07 | | liarwhd 500 | 487/1.06/1.9e-07 | 750/1.63/9.4e-07 | 1168/2.52/8.5e-07 | F/F/2.9e-03 | 268/0.49/1.2e-07 | | liarwhd 1000 | 534/1.43/2.3e-07 | F/F/1.3e-04 | F/F/1.6e-02 | 1267/3.35/9.8e-07 | 294/0.75/4.7e-07 | | liarwhd 10000 | F/F/5.6e-02 | F/F/5.8e+00 | F/F/3.2e+03 | F/F/1.5e+03 | 409/8.96/8.9e-07 | | nondquar 4 | F/F/1.2e-04 | F/F/5.0e-05 | F/F/4.9e-03 | 395/0.66/2.2e-07 | 87/0.12/6.5e-07 | | penalty1 1000 | 15/0.82/1.2e-07 | 15/0.82/1.2e-07 | 15/0.86/1.2e-07 | 15/0.87/1.2e-07 | 15/0.89/1.2e-07 | | penalty1 10000 | 9/28.41/9.6e-07 | 9/28.32/9.6e-07 | 9/28.02/9.6e-07 | 9/28.38/9.6e-07 | 9/28.46/9.6e-07 | | quartc 100 | 22/0.04/5.7e-07 | 23/0.04/6.4e-07 | 34/0.05/7.7e-07 | 28/0.05/1.8e-07 | 60/0.13/1.8e-07 | | quartc 450 | 34/0.14/2.8e-07 | 47/0.20/3.4e-07 | 33/0.14/7.4e-07 | 31/0.12/5.0e-07 | 60/0.31/5.7e-07 |
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