Research Article
A Globally Convergent Hybrid Conjugate Gradient Method and Its Numerical Behaviors
Table 4
Numerical results for test problems from the CUTEr library.
| | Algorithm | #31 (1000) | #32 (1000) | #33 (1000) | #34 (500) | #35 (1024) | #36 (1024) |
| | | MDYHS+ | 18/36/0.013 | 393/685/0.26 | 0/0/0 | 3062/5668/1.87 | 130/213/0.11 | 160/261/0.15 | | MDYHS+1 | 15/22/0.010 | 893/950/0.49 | 0/0/0 | 2200/2218/1.04 | 91/91/0.07 | 118/118/0.09 | | DYHS+ | 13/55/0.020 | 352/945/0.29 | 0/0/0 | 2931/5770/1.76 | 102/214/0.10 | 113/232/0.12 | | | DYHS | 13/55/0.020 | 361/978/0.30 | 0/0/0 | — | 100/210/0.09 | 113/232/0.12 |
| | | MDYHS+ | 38/66/0.03 | 7842/14738/10.49 | 1001/2002/1.29 | 3139/5822/1.94 | 286/524/0.26 | 385/688/0.35 | | MDYHS+1 | 23/30/0.015 | — | 942/942/0.83 | 2378/2396/1.14 | 264/264/0.18 | 228/228/0.16 | | DYHS+ | 25/160/0.054 | 4248/11389/3.86 | 1074/1906/1.20 | 2978/5905/1.82 | 616/1290/0.58 | 287/605/0.27 | | | DYHS | — | — | 907/1631/0.95 | — | 538/1151/0.50 | 295/620/0.28 |
| | | MDYHS+ | 58/106/0.047 | — | 3431/6862/4.30 | 3215/5974/1.99 | 434/820/0.43 | 490/898/0.46 | | MDYHS+1 | 31/38/0.021 | — | 1498/1498/1.32 | 2543/2561/1.21 | 340/340/0.24 | 361/361/0.25 | | DYHS+ | 76/1618/0.52 | — | 4634/19386/9.92 | 3009/6001/1.85 | 1087/2464/1.07 | 466/999/0.44 | | | DYHS | — | — | — | — | 1293/2828/1.18 | 509/1055/0.46 |
| | | MDYHS+ | 70/127/0.057 | — | 5003/10006/6.30 | 3384/6265/2.07 | 498/948/0.48 | 577/1072/0.53 | | MDYHS+1 | 40/47/0.026 | — | 2181/2181/1.92 | 2725/2743/1.31 | 515/1030/0.35 | 471/471/0.33 | | DYHS+ | 181/4886/1.56 | — | — | 3072/6171/1.91 | — | — | | | DYHS | — | — | — | — | — | — |
| | Algorithm | #37 (1000) | #38 (5000) | #39 (500) | #40 (200) | #41 (300) | #42 (3549) |
| | | MDYHS+ | 56/97/0.05 | 5789/9969/32.28 | 1751/3049/1.05 | 47/94/0.23 | 16/32/0.16 | 359/653/81.32 | | MDYHS+1 | 34/59/0.030 | 8454/8547/38.40 | 1093/1141/0.51 | 6/6/0.026 | 4/4/0.03 | 336/337/46.12 | | DYHS+ | 28/141/0.06 | 7487/13997/44.57 | 1332/2982/0.99 | 6/19/0.054 | 4/13/0.06 | 443/861/84.48 | | | DYHS | 51/202/0.09 | 4817/12146/34.72 | 1287/2923/0.82 | 6/19/0.053 | 4/13/0.06 | 492/952/96.01 |
| | | MDYHS+ | 89/163/0.09 | 5793/9973/32.60 | 1770/3087/1.08 | 188/376/0.88 | 26/52/0.26 | 5884/11703/1203.4 | | MDYHS+1 | 45/70/0.04 | 8458/8551/38.59 | 1113/1161/0.53 | 12/12/0.038 | 5/5/0.03 | 7022/7023/964.08 | | DYHS+ | — | 7493/14019/44.41 | 1342/3015/0.93 | 12/39/0.079 | 5/16/0.07 | 8060/15523/1508.6 | | | DYHS | — | 4822/12166/34.68 | 1297/2957/0.80 | 12/39/0.079 | 5/16/0.07 | 8684/16652/1662.2 |
| | | MDYHS+ | 141/263/0.14 | 5800/9987/32.43 | 1790/3127/1.09 | 527/1054/2.51 | 36/72/0.36 | 24741/49417/5064.2 | | MDYHS+1 | 52/77/0.05 | 8458/8551/38.59 | 1124/1172/0.54 | 34/34/0.11 | 6/6/0.04 | 25795/25796/3494.0 | | DYHS+ | — | 7493/14019/44.48 | — | 1037/2829/5.45 | 6/19/0.08 | — | | | DYHS | — | 4824/12173/34.70 | — | 2256/6052/11.57 | 6/19/0.08 | — |
| | | MDYHS+ | 182/331/0.18 | 5810/10007/32.52 | 1873/3267/1.16 | 1057/2114/4.99 | 46/92/0.48 | 43624/87169/8874.9 | | MDYHS+1 | 64/89/0.05 | 8459/8552/38.66 | 1135/1183/0.55 | 72/72/0.22 | 7/7/0.05 | 44983/44984/6104.9 | | DYHS+ | — | 7494/14022/44.62 | — | 5969/16319/32.19 | 7/23/0.09 | — | | | DYHS | — | 4824/12173/34.68 | — | — | 7/23/0.09 | — |
| | Algorithm | #43 (5000) | #44 (150) | #45 (200) | #46 (529) | #47 (500) | #48 (1010) |
| | | MDYHS+ | 110/207/0.35 | 38/75/1.05 | 210/374/0.12 | 217/386/0.44 | 7/14/0.004 | 508/860/1.74 | | MDYHS+1 | 586/602/1.37 | 8/8/0.15 | 169/226/0.08 | 298/310/0.46 | 9/9/0.004 | 466/486/1.22 | | DYHS+ | 19/66/0.08 | 8/26/0.32 | 87/272/0.08 | 311/658/0.66 | 10/24/0.007 | 361/1091/1.69 | | | DYHS | 219/599/0.78 | 8/26/0.31 | 177/533/0.14 | 295/628/0.62 | 10/24/0.007 | 481/1370/2.15 |
| | | MDYHS+ | 127/241/0.41 | 44/86/1.10 | 310/569/0.18 | 4916/9716/10.94 | 468/936/0.28 | 1331/2492/4.76 | | MDYHS+1 | 859/875/1.99 | 10/10/0.17 | 261/318/0.12 | 2367/2379/3.64 | 516/516/0.22 | 556/576/1.50 | | DYHS+ | 21/72/0.10 | 11/36/0.41 | 156/476/0.13 | 7103/13549/13.28 | 495/924/0.27 | — | | | DYHS | 246/679/0.91 | 11/36/0.41 | 326/977/0.25 | 7129/13668/13.33 | 350/673/0.21 | — |
| | | MDYHS+ | 136/257/0.43 | — | 406/761/0.25 | 6880/13644/15.12 | 21368/42736/12.82 | 1453/2736/5.31 | | MDYHS+1 | 1147/1163/2.79 | — | 362/419/0.17 | 3956/3968/6.02 | 18659/18659/8.30 | 646/666/1.67 | | DYHS+ | 22/75/0.10 | — | 189/579/0.16 | 13395/25751/25.48 | — | — | | | DYHS | 262/730/0.96 | — | 498/1497/0.42 | 16291/31452/32.49 | — | — |
| | | MDYHS+ | 141/263/0.45 | — | 593/1030/0.34 | 8837/17436/19.87 | 46983/93966/29.49 | 1773/3332/6.32 | | MDYHS+1 | 1294/1310/3.06 | — | 491/548/0.23 | 5994/6006/9.58 | 42158/42158/19.46 | 859/879/2.23 | | DYHS+ | — | — | 330/999/0.28 | 21089/40486/39.78 | — | — | | | DYHS | 268/749/0.10 | — | 644/1930/0.53 | 26127/50417/49.36 | — | — |
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