Research Article
A Globally Convergent Hybrid Conjugate Gradient Method and Its Numerical Behaviors
Table 2
Numerical results for test problems from the CUTEr library.
| | Algorithm | #1 (1000) | #2 (500) | #2 (1000) | #3 (1000) | #3 (5000) | #4 (2000) |
| | | MDYHS+ | 21/36/0.015 | 134/221/0.086 | 102/166/0.09 | 533/1066/0.34 | 738/1476/1.48 | 31/62/0.05 | | MDYHS+1 | 6/19/0.005 | 99/109/0.056 | 75/98/0.06 | 500/500/0.23 | 1999/1999/2.99 | 9/14/0.015 | | DYHS+ | 3/7/0.003 | 89/238/0.080 | 77/209/0.11 | 255/412/0.14 | 255/412/0.44 | 8/73/0.05 | | | DYHS | 4/9/0.004 | 108/274/0.093 | 187/477/0.23 | 255/412/0.14 | 255/412/0.42 | 15/93/0.06 |
| | | MDYHS+ | 41/76/0.031 | 177/307/0.13 | 163/288/0.15 | 738/2214/0.49 | 2738/5476/5.54 | 82/104/0.09 | | MDYHS+1 | 8/21/0.007 | 172/182/0.09 | 106/129/0.09 | 500/500/0.25 | 2500/2500/3.76 | 11/16/0.016 | | DYHS+ | 7/68/0.029 | 851/20742/5.97 | 427/8252/3.37 | 3884/6188/2.29 | 13726/22027/22.90 | — | | | DYHS | 5/11/0.005 | — | — | 4048/6461/2.42 | 13759/22098/22.98 | 24/166/0.12 |
| | | MDYHS+ | 61/11/0.051 | 228/409/0.15 | 214/390/0.20 | 1299/2598/0.82 | 3923/7846/8.05 | 68/204/0.13 | | MDYHS+1 | 8/21/0.007 | 251/261/0.145 | 139/162/0.11 | 500/500/0.25 | 2501/2501/3.73 | 12/17/0.018 | | DYHS+ | 7/68/0.028 | 1223/30509/9.06 | 900/20509/8.28 | 8831/14347/5.34 | 44013/71661/74.32 | — | | | DYHS | — | — | — | 7754/12601/4.07 | 42394/69153/71.49 | — |
| | | MDYHS+ | 80/153/0.068 | 307/549/0.20 | 318/581/0.28 | 1579/3157/1.00 | 5817/11634/11.85 | 99/192/0.17 | | MDYHS+1 | 12/54/0.016 | 323/3330.17 | 248/271/0.19 | 502/502/0.22 | 2504/2504/3.81 | 33/38/0.043 | | DYHS+ | — | 3020/77907/22.34 | 1618/36542/14.75 | 13400/21926/7.40 | — | — | | | DYHS | — | — | — | 12338/20212/6.60 | — | — |
| | Algorithm | #5 (1000) | #6 (200) | #7 (5000) | #8 (100) | #9 (150) | #10 (1000) |
| | | MDYHS+ | 367/643/0.81 | 27/53/0.03 | 35/57/0.15 | 248/453/0.12 | 9/14/0.004 | 66/93/0.08 | | MDYHS+1 | 310/316/0.50 | 3/14/0.006 | 37/70/0.16 | 230/247/0.08 | 6/14/0.004 | 70/91/0.08 | | DYHS+ | 322/545/0.66 | 2/4/0.007 | 57/152/0.32 | 289/669/0.15 | 8/35/0.009 | 61/155/0.11 | | | DYHS | 321/553/0.67 | 2/9/0.007 | 55/148/0.30 | 307/701/0.17 | 8/35/0.009 | 58/154/0.11 |
| | | MDYHS+ | 392/693/0.83 | 54/105/0.06 | 55/97/0.23 | 347/651/0.16 | 18/32/0.008 | 104/169/0.14 | | MDYHS+1 | 334/340/0.54 | 8/19/0.010 | 45/78/0.19 | 398/415/0.14 | 9/17/0.005 | 109/130/0.12 | | DYHS+ | 352/868/0.96 | 14/42/0.03 | 92/223/0.48 | 438/996/0.23 | 11/45/0.010 | 200/3163/2.11 | | | DYHS | 339/595/0.72 | 14/42/0.03 | 96/232/0.50 | 456/1028/0.25 | 11/45/0.010 | — |
| | | MDYHS+ | 414/737/0.88 | 842/1355/0.88 | 75/137/0.33 | 471/899/0.22 | 28/52/0.012 | 142/245/0.19 | | MDYHS+1 | 357/363/0.58 | 9/20/0.011 | 54/87/0.22 | 561/578/0.22 | 13/21/0.006 | 150/171/0.16 | | DYHS+ | 442/3072/3.01 | 20/59/0.04 | 135/309/0.68 | — | 31/93/0.022 | 573/13215/8.23 | | | DYHS | — | 20/59/0.04 | 137/322/0.70 | — | 155/390/0.083 | — |
| | | MDYHS+ | 436/778/0.93 | — | 95/177/0.42 | 612/1128/0.32 | 36/67/0.016 | 187/322/0.26 | | MDYHS+1 | 379/385/0.61 | — | 62/95/0.25 | 724/741/0.26 | 16/24/0.007 | 193/214/0.21 | | DYHS+ | — | — | 167/376/0.82 | — | — | — | | | DYHS | — | — | 171/398/0.88 | — | — | — |
| | Algorithm | #11 (1000) | #12 (1000) | #13 (1000) | #14 (3000) | #15 (3000) | #16 (1500) |
| | | MDYHS+ | 3764/7333/2.91 | 5422/10414/5.14 | 6065/11565/6.74 | 15/26/0.03 | 10/14/0.02 | 13/20/0.011 | | MDYHS+1 | 4199/4222/2.42 | 4950/4979/3.54 | 5796/5826/4.68 | 6/14/0.015 | 7/18/0.020 | 8/23/0.009 | | DYHS+ | 7418/14260/5.42 | 8775/17315/8.59 | 13564/27163/15.10 | 4/17/0.015 | 4/18/0.017 | 4/22/0.009 | | | DYHS | 8798/16878/6.07 | 9565/18913/8.71 | 11328/22680/11.97 | 4/17/0.016 | 4/18/0.016 | 4/24/0.009 |
| | | MDYHS+ | 6334/12473/4.99 | 9030/17630/8.73 | 1004/19523/11.08 | 24/44/0.05 | 20/34/0.039 | 24/42/0.022 | | MDYHS+1 | 6768/6791/3.88 | 9230/9259/6.83 | 10415/10445/8.34 | 7/15/0.020 | 8/19/0.020 | 9/24/0.010 | | DYHS+ | — | — | — | 5/20/0.02 | 5/21/0.021 | 5/26/0.010 | | | DYHS | — | — | — | 6/22/0.02 | 5/21/0.020 | 6/29/0.011 |
| | | MDYHS+ | 9104/18013/7.15 | 12496/24559/12.32 | 12979/25367/14.46 | 34/64/0.07 | 30/54/0.061 | 34/62/0.031 | | MDYHS+1 | 9806/9829/6.02 | 12937/12966/8.85 | 14193/14223/11.29 | 8/16/0.022 | 9/20/0.021 | 10/25/0.011 | | DYHS+ | — | — | — | 38/807/0.70 | 6/24/0.022 | 8/35/0.014 | | | DYHS | — | — | — | — | 7/27/0.025 | 8/35/0.014 |
| | | MDYHS+ | — | — | — | 44/84/0.09 | 41/76/0.087 | 45/84/0.041 | | MDYHS+1 | 13775/13798/8.59 | — | — | 10/18/0.024 | 10/21/0.0222 | 12/27/0.013 | | DYHS+ | — | — | — | 109/2633/2.32 | 9/30/0.037 | 141/533/0.212 | | | DYHS | — | — | — | — | 8/29/0.034 | 22/71/0.03 |
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