一个改进的WYL型三项共轭梯度法
朱志斌,耿远航

A Modified Three-Term WYL Conjugate Gradient Method
Zhibin Zhu,Yuanhang Geng
表 2 数值结果
N D MPRP WYL MWYL HZ TWYL
$ k $   $ q $   $ r $   $ t $ $ k $   $ q $   $ r $   $ t $ $ k $   $ q $   $ r $   $ t $ $ k $   $ q $   $ r $   $ t $ $ k $   $ q $   $ r $   $ t $
1 10 23/24/24/0.0040 99/1059/3218/0.0191 13/106/198/0.0053 20/110/197/0.0099 16/17/17/0.0019
600 21/22/22/0.0120 73/1151/2228/0.0342 18/100/181/0.0073 15/98/178/0.0172 11/12/12/0.0071
1000 15/16/16/0.0047 61/933/1804/0.0348 18/100/181/0.0049 13/86/156/0.0154 12/13/13/0.0042
2 5 28/29/29/0.0016 29/267/504/0.0029 34/140/245/0.0018 25/129/230/0.0092 19/20/20/0.0012
20 30/31/31/0.0024 91/1606/3120/0.0158 24/185/345/0.0023 24/149/271/0.0102 20/21/21/0.0016
100 46/47/47/0.0061 26/254/481/0.0059 25/210/394/0.0052 21/166/308/0.0095 21/22/22/0.0037
3 100 264/265/265/0.0051 5768/83377/16098/0.1955 270/2520/4769/0.0075 322/3115/5905/0.0416 169/170/170/0.0040
500 220/221/221/0.0140 2154/28471/54787/0.2580 426/3895/7363/0.0377 525/5062/9596/0.0865 213/214/214/0.0141
1000 264/265/265/0.0298 7223/96621/186018/1.5034 381/3500/6618/0.0566 440/4268/8093/0.0871 251/252/252/0.0288
4 10 30/31/31/8.4960e-4 37/320/602/0.0013 26/144/261/8.5290e-4 32/145/255/0.0074 22/23/23/6.8260e-4
100 47/48/48/0.0033 210/2749/5287/0.0257 46/342/637/0.0045 50/341/629/0.0145 40/41/41/0.0031
1000 65/66/66/0.0505 84/968/1851/0.0765 70/601/1251/0.0521 93/898/1700/0.0721 64/65/65/0.0412
5 10 39/40/40/0.0012 87/1845/3602/0.0035 37/174/310/7.8290e-4 44/233/419/0.0093 31/32/32/7.1240e-4
100 128/129/129/0.0026 134/1393/2651/0.0046 115/851/1586/0.0031 131/999/1864/0.0224 102/103/103/0.0020
1000 368/369/369/0.0483 480/7022/13563/0.1182 402/4059/7715/0.0697 545/5637/10726/0.1131 337/338/338/0.0465
6 10 33/34/34/0.0014 28/205/381/0.0017 39/159/278/0.0016 28/130/229/0.0063 20/21/21/0.0012
100 65/66/66/0.0058 69/603/1136/0.0095 41/272/502/0.0051 68/470/869/0.0206 45/46/46/0.0044
1000 80/81/81/0.0667 86/1026/1965/0.1169 66/615/1136/0.0704 78/756/1431/0.0744 71/72/72/0.0616
7 10 53/54/54/0.0032 32/303/573/0.0039 34/195/355/0.0033 31/190/346/0.0073 30/31/31/0.0020
100 40/41/41/0.0062 400/7132/13863/0.4381 31/184/336/0.0069 27/164/298/0.0078 23/24/24/0.0034
1000 27/28/28/0.0104 30/329/627/0.0292 42/241/439/0.0250 23/140/254/0.0188 19/20/20/0.0078
10000 23/24/24/0.0718 275/5356/10436/4.7556 26/150/273/0.1357 18/111/201/0.0889 14/15/15/0.0452
20000 23/24/24/0.1684 28/310/591/0.5345 26/148/269/0.2359 16/97/175/0.1371 12/13/13/0.0840
8 10 38/39/39/8.1400e-4 1171/15199/29226/0.0249 74/470/865/0.0013 50/359/665/0.0082 51/52/52/7.4680e-4
500 42/43/43/0.0021 1315/16667/32018/0.0818 63/398/732/0.0024 54/389/721/0.0062 57/58/58/0.0018
1000 39/40/40/0.0033 1341/16869/32396/0.2188 70/442/813/0.0064 82/584/1083/0.0117 62/63/63/0.0048
9 10 3/4/4/0.0011 3/7/10/0.0011 5/11/16/9.2270e-4 7/22/34/0.0016 3/4/4/8.9320e-4
100 3/4/4/0.0013 3/7/10/0.0010 5/11/16/0.0013 6/19/29/0.0021 3/4/4/0.0010
10 10 48/49/49/0.0017 42/665/1287/0.0029 54/363/671/0.0020 22/165/305/0.0077 23/24/24/0.0012
100 52/53/53/0.0020 46/728/1409/0.0037 57/383/708/0.0026 31/230/426/0.0045 23/24/24/0.0013
1000 56/57/57/0.0054 48/758/1467/0.0134 58/390/721/0.0074 27/199/368/0.0054 25/26/26/0.0030
10000 56/57/57/0.0579 52/815/1577/0.1831 58/390/721/0.1078 31/232/430/0.0928 29/30/30/0.0517
11 10 16/17/17/0.0014 15/58/100/0.0013 30/139/247/0.0018 18/79/137/0.0034 16/17/17/0.0011
100 15/16/16/0.0016 15/58/100/0.0014 29/134/238/0.0022 16/72/125/0.0039 15/16/16/0.0014
1000 15/16/16/0.0039 13/51/88/0.0041 28/130/231/0.0085 16/72/125/0.0052 14/15/15/0.0035
12 10 37/38/38/9.3410e-4 61/1124/2186/0.0035 27/119/210/0.0018 28/145/259/0.0046 27/28/28/8.0080e-4
100 39/40/40/0.0013 65/1175/2284/0.0051 27/119/210/0.0012 30/156/279/0.0052 28/29/29/9.8960e-4
1000 39/40/40/0.0038 69/1223/2376/0.0261 28/124/219/0.0034 32/166/297/0.0093 30/31/31/0.0033
13 1000 376/377/377/0.0308 468/5435/10401/0.0547 454/4196/7937/0.0429 462/4369/8273/0.1338 307/308/308/0.0249
10000 1316/1317/1317/3.1568 1620/24780/47939/5.6254 2791/33598/64404/8.2298 1663/20450/39234/7.6030 1135/1136/1136/1.6381
20000 2089/2090/2090/5.7360 3224/56220/109215/16.2122 4791/61853/118914/18.7639 2321/30644/58964/22.2503 1613/1614/1614/4.8625
14 10 54/55/55/0.0011 121/1623/3124/0.0038 38/219/399/0.0013 42/257/469/0.0075 32/33/33/8.5090e-4
600 321/322/322/0.0206 5682/137079/268475/1.1904 327/3383/6438/0.0317 392/4137/7879/0.0521 265/266/266/0.0185
1000 396/397/397/0.0399 501/7736/14970/0.0992 469/5196/9922/0.0701 518/5796/11071/0.0852 348/349/349/0.0378
15 10 60/61/61/0.0019 81/1739/3396/0.0056 13/115/216/9.7820e-4 23/231/436/0.0053 17/18/18/8.4180e-4
100 55/56/56/0.0030 73/1587/3100/0.0104 12/106/199/0.0019 21/211/398/0.0052 16/17/17/0.0017
1000 49/50/50/0.0122 65/1426/2786/0.0520 11/97/182/0.0040 17/171/322/0.0070 16/17/17/0.0043
16 1000 42/43/43/0.0042 33/167/300/0.0062 26/86/145/0.0037 36/142/245/0.0076 26/27/27/0.0034
10000 36/37/37/0.0337 15/127/238/0.0404 12/43/73/0.0176 14/61/105/0.0233 15/16/16/0.0210
20000 32/33/33/0.0580 12/76/139/0.0512 11/40/68/0.0270 10/47/81/0.0316 10/11/11/0.0240
100000 24/25/25/0.1614 9/58/106/0.1309 9/33/56/0.0811 7/36/62/0.0756 9/10/10/0.0670
17 1000 1/2/2/0.0149 1000/20044/30088/9.3673 1000/20001/30002/9.2210 -/-/-/- 1/2/2/0.0068
18 10 35/36/36/0.0033 93/2021/3948/0.0291 27/136/244/0.0029 26/139/249/0.0066 24/25/25/0.0027
100 75/76/76/0.0359 80/802/1523/0.0908 72/540/1007/0.0594 86/673/1257/0.1408 72/73/73/0.0319
1000 334/335/335/51.9645 348/5448/10547/98.1685 389/4631/8872/78.6427 491/5943/11392/90.9052 305/306/306/32.5759
19 10 36/37/37/8.8550e-4 89/1945/3800/0.0081 33/157/280/9.2980e-4 43/226/406/0.0050 31/32/32/7.7060e-4
100 118/119/119/0.0059 142/1620/3097/0.0110 116/855/1593/0.0068 128/965/1799/0.0209 104/105/105/0.0051
1000 365/366/366/0.0464 512/7484/14455/0.1206 400/4038/7675/0.0666 469/4841/9210/0.0901 325/326/326/0.0434
10000 1140/1141/1141/2.2828 2024/36184/70343/7.2277 2630/33971/65311/6.6585 1606/21180/40751/7.7436 1115/1116/1116/2.3376
20 10 111/112/112/0.0038 645/6679/12712/0.0377 88/550/1011/0.0041 120/795/1467/0.0197 104/105/105/0.0036
50 581/582/582/0.0448 7249/75221/143192/0.8142 720/7177/13633/0.0812 649/6657/12662/0.1175 526/527/527/0.0433
100 1389/1390/1390/1.1858 1461/23309/45156/1.9609 1580/18355/35129/1.7259 1436/17161/32883/0.4488 1096/1097/1097/0.6747
21 1000 23/24/24/0.0713 26/317/607/0.0249 8/24/39/0.0027 10/41/69/0.0167 12/13/13/0.0040
10000 30/31/31/0.0016 20/227/433/1.5810 7/21/34/0.1396 9/37/62/0.0854 9/10/10/0.1825
20000 24/25/25/0.5173 20/226/431/3.2724 7/21/34/0.2893 9/37/62/0.1277 9/10/10/0.3605
22 100 30/31/31/0.0016 18/183/347/0.0025 11/32/54/0.0011 12/49/83/0.0042 11/12/12/0.0011
10000 24/25/25/0.0418 12/106/199/0.0825 9/27/44/0.0197 10/41/69/0.0476 8/9/9/0.0189
20000 23/24/24/0.0713 10/83/155/0.1243 9/27/44/0.0377 10/41/69/0.0590 8/9/9/0.0342
23 10000 103/104/104/0.8917 101/1647/3192/1.1939 92/1200/2307/0.9328 94/1242/2387/0.8362 91/92/92/0.7481
20000 59/60/60/0.8852 73/1302/2530/1.8032 68/895/1721/1.2813 -/-/-/- 58/59/59/0.8296
100000 64/65/65/5.0643 108/2333/4557/15.1715 71/1174/2276/7.5531 -/-/-/- 54/55/55/4.3003
24 10000 20/21/21/0.0138 137/3270/6402/0.5786 20/63/105/0.0138 30/122/211/0.0609 18/19/19/0.0110
15000 23/24/24/0.0203 137/3261/6384/1.0262 19/60/100/0.0261 31/124/214/0.0910 21/22/22/0.0210
20000 22/23/23/0.0324 137/3253/6368/1.2361 19/58/96/0.0228 31/124/214/0.1063 18/19/19/0.0199
25 50 36/37/37/0.0019 243/5487/10730/0.0282 17/113/208/0.0081 46/370/691/0.0127 18/19/19/0.0014
100 37/38/38/0.0200 103/2346/4588/0.0313 23/176/328/0.0025 30/270/507/0.0125 25/26/26/0.0095
1000 449/450/450/0.2043 72/1683/3293/0.0947 -/-/-/- 29/345/658/0.0351 15/16/16/0.0153
26 10000 14/15/15/0.0301 12/47/81/0.0342 28/130/231/0.1007 15/67/116/0.0788 12/13/13/0.0321
20000 14/15/15/0.0546 12/47/81/0.0696 28/129/229/0.1529 15/67/116/0.1037 11/12/12/0.0477
100000 13/14/14/0.2266 11/44/76/0.2716 27/126/224/0.6975 11/50/86/0.2511 11/12/12/0.2078
27 100 46/47/47/0.0035 55/656/1256/0.0103 25/253/480/0.0049 -/-/-/- 19/20/20/0.0020
1000 23/24/24/0.0197 73/1332/2590/0.1416 16/162/307/0.0195 -/-/-/- 14/15/15/0.0071
10000 16/17/17/0.0686 106/1118/2129/1.2885 15/114/212/0.1380 -/-/-/- 15/16/16/0.0618
28 10000 64/65/65/0.2786 73/808/1542/0.4350 48/452/855/0.2320 73/712/1348/0.4219 58/59/59/0.2042
50000 55/56/56/1.1709 159/2313/4466/4.1139 46/527/1007/1.3277 86/1025/1961/3.5063 40/41/41/0.8828
100000 45/46/46/2.0890 45/735/1460/3.7004 49/605/1160/2.8631 39/488/934/3.8924 33/34/34/1.6141
29 1000 30/31/31/0.0209 25/175/324/0.0167 28/147/265/0.0141 26/142/255/0.0237 22/23/23/0.0099
10000 21/22/22/0.1070 52/774/1495/0.7530 22/152/281/0.1586 21/150/276/0.1327 21/22/22/0.1054
20000 20/21/21/0.2274 22/308/593/0.5727 19/182/344/0.3380 21/153/282/0.2527 19/20/20/0.2101