Research Article
A Globally Convergent Hybrid Conjugate Gradient Method and Its Numerical Behaviors
Table 5
Numerical results for test problems from the CUTEr library.
| | Algorithm | #49 (500) | #49 (2000) | #50 (1000) | #51 (100) | #52 (10000) | #53 (100) |
| | | MDYHS+ | 79/134/0.14 | 74/129/0.48 | 1877/3565/1.93 | 237/394/0.10 | 23/44/0.10 | 94/129/0.03 | | MDYHS+1 | 68/71/0.11 | 73/78/0.36 | 884/884/0.65 | 106/106/0.04 | 3/9/0.02 | 156/169/0.06 | | DYHS+ | 58/151/0.13 | 60/167/0.48 | 3154/6174/3.13 | 276/614/0.13 | 2/6/0.012 | 103/291/0.06 | | | DYHS | 65/173/0.14 | 48/143/0.41 | 1334/2566/1.31 | 246/545/0.12 | 2/6/0.012 | 94/256/0.05 |
| | | MDYHS+ | 3234/6363/6.58 | 3110/6127/21.04 | 2844/5499/2.98 | 347/614/0.16 | 44/85/0.20 | 2168/3506/0.87 | | MDYHS+1 | 3169/3172/4.46 | 5088/5093/24.20 | 1887/1887/1.43 | 208/208/0.07 | 9/27/0.05 | 11836/11849/4.06 | | DYHS+ | — | 3885/35556/80.37 | 9989/19969/10.11 | 526/1135/0.26 | 6/19/0.042 | 1242/3710/0.71 | | | DYHS | — | — | 9642/18822/9.61 | 462/1012/0.25 | 10/32/0.062 | 1410/4146/0.82 |
| | | MDYHS+ | 4046/7987/8.24 | 4207/8321/28.92 | 3751/7313/4.08 | 462/844/0.21 | 51/97/0.23 | 27768/50730/12.06 | | MDYHS+1 | 5957/5960/8.40 | 10111/10116/48.22 | 2824/2824/2.14 | 282/282/0.10 | 21/48/0.10 | — | | DYHS+ | — | — | — | — | 8/25/0.05 | 5250/15889/3.02 | | | DYHS | — | — | — | — | 11/35/0.07 | 20679/62630/12.10 |
| | | MDYHS+ | 5708/11097/11.51 | 5876/11485/40.39 | 5034/9605/5.23 | 546/1010/0.26 | — | — | | MDYHS+1 | 8594/8597/12.12 | 15076/15081/71.84 | 3598/3598/2.78 | 357/357/0.13 | — | — | | DYHS+ | — | — | — | — | — | 12363/37959/7.59 | | | DYHS | — | — | — | — | — | — |
| | Algorithm | #54 (10000) | #55 (500) | #56 (100) | #57 (5000) | #58 (100) | #59 (1000) |
| | | MDYHS+ | 32/52/0.11 | 22/22/0.009 | 40/52/0.026 | 90/152/0.23 | 39/45/0.021 | 21/21/0.010 | | MDYHS+1 | 24/33/0.08 | 22/22/0.009 | 42/49/0.021 | 205/217/0.31 | 41/46/0.025 | 21/25/0.009 | | DYHS+ | 20/75/0.12 | 2/60/0.012 | 39/165/0.062 | 54/168/0.21 | 34/165/0.051 | 29/220/0.051 | | | DYHS | 22/78/0.13 | 3/59/0.012 | 37/165/0.041 | 54/168/0.21 | 30/153/0.042 | 24/161/0.048 |
| | | MDYHS+ | 52/92/0.20 | 62/97/0.029 | 109/165/0.059 | 631/1197/1.37 | 59/65/0.022 | 26/26/0.011 | | MDYHS+1 | 36/45/0.11 | 62/100/0.030 | 80/87/0.037 | 3455/3467/5.14 | 60/65/0.020 | 26/30/0.011 | | DYHS+ | 32/110/0.18 | 18/175/0.039 | 115/1226/0.31 | 179/548/0.47 | 47/218/0.042 | 37/296/0.064 | | | DYHS | 34/111/0.18 | 30/426/0.092 | — | 239/707/0.56 | 46/217/0.034 | 32/222/0.047 |
| | | MDYHS+ | 72/132/0.28 | 87/170/0.048 | 156/259/0.095 | 1479/2854/2.92 | 79/85/0.027 | 30/30/0.013 | | MDYHS+1 | 48/57/0.15 | 185/412/0.079 | 120/127/0.055 | — | 79/84/0.028 | 30/34/0.013 | | DYHS+ | 44/150/0.25 | 22/187/0.042 | — | 210/655/0.56 | 56/272/0.046 | 43/327/0.071 | | | DYHS | 47/153/0.26 | 38/451/0.099 | — | 405/1192/0.95 | 60/263/0.041 | 38/245/0.055 |
| | | MDYHS+ | 83/150/0.33 | 107/210/0.069 | 209/363/0.13 | 2541/4941/5.05 | 99/105/0.033 | 35/35/0.015 | | MDYHS+1 | 61/70/0.19 | 315/357/0.13 | 160/167/0.07 | — | 99/104/0.031 | 35/39/0.015 | | DYHS+ | 55/187/0.30 | 23/191/0.042 | — | 227/720/0.62 | 70/334/0.053 | 46/345/0.074 | | | DYHS | 58/188/0.31 | 49/556/0.121 | — | 571/1672/1.34 | 78/325/0.054 | 45/303/0.064 |
| | Algorithm | #59 (10000) | #60 (1000) | #60 (5000) | #61 (100) | #62 (5000) | #62 (10000) |
| | | MDYHS+ | 25/25/0.060 | 34/59/0.059 | 31/60/0.27 | 41/77/0.53 | 14/14/0.051 | 15/15/0.106 | | MDYHS+1 | 25/25/0.060 | 22/23/0.030 | 23/27/0.15 | 50/64/0.52 | 14/26/0.071 | 15/26/0.141 | | DYHS+ | 56/317/0.34 | 28/70/0.061 | 27/73/0.29 | 21/73/0.45 | 25/139/0.24 | 39/222/0.716 | | | DYHS | 51/343/0.35 | 28/71/0.062 | 26/68/0.27 | 21/73/0.45 | 28/161/0.27 | 33/201/0.627 |
| | | MDYHS+ | 29/29/0.065 | 58/107/0.10 | 55/108/0.49 | 53/101/0.65 | 19/19/0.068 | 20/20/0.139 | | MDYHS+1 | 29/29/0.065 | 40/41/0.06 | 40/44/0.27 | 54/68/0.55 | 19/31/0.084 | 19/30/0.168 | | DYHS+ | 68/377/0.42 | 56/144/0.13 | 67/162/0.64 | 26/90/0.55 | 36/203/0.346 | 53/311/1.005 | | | DYHS | 62/406/0.41 | 52/180/0.14 | 51/133/0.51 | 26/90/0.55 | 34/199/0.341 | 41/242/0.758 |
| | | MDYHS+ | 34/34/0.070 | 80/151/0.15 | 77/152/0.68 | 63/119/0.83 | 24/24/0.085 | 24/24/0.175 | | MDYHS+1 | 34/34/0.070 | 57/58/0.07 | 58/62/0.36 | 58/72/0.61 | 23/35/0.103 | 24/35/0.210 | | DYHS+ | 77/441/0.46 | — | — | 87/647/3.52 | 45/252/0.43 | 67/380/1.212 | | | DYHS | 70/462/0.46 | 7087/16410/14.10 | 15757/35456/138.93 | — | 46/278/0.448 | 52/304/0.962 |
| | | MDYHS+ | 39/39/0.09 | 104/197/0.18 | 106/202/0.92 | — | 28/28/0.103 | 29/29/0.203 | | MDYHS+1 | 39/39/0.09 | 74/75/0.10 | 74/78/0.46 | — | 28/40/0.12 | 29/40/0.241 | | DYHS+ | 83/477/0.52 | — | — | — | 56/321/0.536 | 80/462/1.479 | | | DYHS | 82/535/0.53 | — | — | — | 51/310/0.506 | 61/356/1.123 |
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