Research Article
A Globally Convergent Hybrid Conjugate Gradient Method and Its Numerical Behaviors
Table 3
Numerical results for test problems from the CUTEr library.
| | Algorithm | #17 (3000) | #18 (3000) | #18 (6000) | #19 (3000) | #19 (9000) | #20 (3000) |
| | | MDYHS+ | 15/23/0.022 | 81/155/0.17 | 90/173/0.29 | 31/42/0.05 | 31/42/0.11 | 27/36/0.045 | | MDYHS+1 | 9/28/0.027 | 70/77/0.12 | 80/87/0.21 | 66/76/0.12 | 44/54/0.16 | 61/76/0.101 | | DYHS+ | 5/27/0.021 | 61/90/0.15 | 61/146/0.22 | 22/70/0.06 | 41/108/0.21 | 38/102/0.096 | | | DYHS | 5/27/0.021 | 60/86/0.12 | 60/140/0.20 | 30/88/0.07 | 35/93/0.18 | 29/82/0.072 |
| | | MDYHS+ | 26/45/0.054 | 235/463/0.51 | 317/627/1.08 | 278/513/0.57 | 453/845/2.09 | 214/391/0.46 | | MDYHS+1 | 11/30/0.029 | 229/236/0.38 | 310/317/0.78 | 176/186/0.28 | 279/289/0.93 | 177/192/0.28 | | DYHS+ | 7/33/0.03 | 315/400/0.62 | 373/759/1.19 | 287/608/0.60 | 473/958/2.03 | 252/527/0.52 | | | DYHS | 8/37/0.031 | 321/420/0.66 | 434/884/1.28 | 275/564/0.52 | 487/979/2.15 | 243/503/0.50 |
| | | MDYHS+ | 36/65/0.071 | 322/637/0.72 | 443/879/1.50 | 457/871/0.99 | 740/1419/3.43 | 381/725/0.81 | | MDYHS+1 | 13/32/0.033 | 317/324/0.51 | 432/439/1.09 | 332/342/0.52 | 508/518/1.70 | 320/335/0.53 | | DYHS+ | 9/40/0.031 | 591/1166/1.21 | 991/1993/3.13 | 647/1334/1.37 | 1004/2179/4.47 | 458/919/0.95 | | | DYHS | 10/43/0.036 | 564/1209/1.14 | 797/1593/2.34 | 527/1200/1.07 | 982/2089/4.06 | 529/1133/1.12 |
| | | MDYHS+ | 46/85/0.10 | 461/915/1.00 | 609/1211/2.10 | 614/1185/1.33 | 984/1907/4.57 | 517/997/1.08 | | MDYHS+1 | 15/34/0.035 | 379/386/0.63 | 529/536/1.34 | 462/472/0.78 | 779/789/2.60 | 465/480/0.79 | | DYHS+ | 54/949/0.71 | — | — | — | — | — | | | DYHS | 285/698/0.61 | — | — | — | — | — |
| | Algorithm | #20 (9000) | #21 (3000) | #22 (300) | #23 (300) | #24 (300) | #25 (1500) |
| | | MDYHS+ | 26/34/0.52 | 23/29/0.04 | 89/170/0.047 | 29/39/0.012 | 29/39/0.012 | 27/37/0.02 | | MDYHS+1 | 38/53/0.15 | 59/78/0.12 | 102/109/0.042 | 37/47/0.016 | 40/54/0.021 | 42/61/0.03 | | DYHS+ | 17/38/0.11 | 21/72/0.06 | 101/231/0.057 | 36/60/0.023 | 26/78/0.018 | 30/92/0.04 | | | DYHS | 30/89/0.16 | 27/83/0.07 | 98/222/0.050 | 28/79/0.017 | 26/78/0.016 | 27/85/0.035 |
| | | MDYHS+ | 395/735/1.78 | 261/484/0.55 | 525/1042/0.30 | 706/1358/0.37 | 785/1486/0.40 | 2363/4633/2.32 | | MDYHS+1 | 274/289/0.97 | 177/196/0.29 | 485/492/0.21 | 400/410/0.16 | 430/444/0.17 | 1425/1444/1.03 | | DYHS+ | 334/674/1.40 | 283/611/0.59 | 1267/2465/0.63 | 1000/1856/0.49 | 989/1893/0.49 | 273/568/0.27 | | | DYHS | 347/723/1.43 | 259/545/0.48 | 1385/2676/0.65 | 1050/2041/0.51 | 1290/2479/0.58 | 289/602/0.26 |
| | | MDYHS+ | 688/1321/3.19 | 436/834/0.93 | 685/1362/0.38 | 1281/2508/0.69 | 1236/2388/0.65 | 3799/7505/3.72 | | MDYHS+1 | 475/490/1.63 | 316/336/0.53 | 578/585/0.23 | 890/900/0.40 | 929/943/0.37 | 3539/3558/2.58 | | DYHS+ | 1131/2375/4.87 | 500/1039/1.02 | 2892/6062/1.58 | 2920/5644/1.53 | 2425/4934/1.32 | 10163/19925/9.19 | | | DYHS | 1027/2087/4.14 | 553/1123/1.07 | 3361/6720/1.74 | 2681/5228/1.40 | 3045/6257/1.55 | 12152/24343/10.54 |
| | | MDYHS+ | 899/1743/4.17 | 591/1144/1.27 | 995/1982/0.55 | 1822/3590/1.03 | 1753/3422/0.97 | 5812/11531/5.71 | | MDYHS+1 | 767/782/2.59 | 462/481/0.75 | 940/947/0.37 | 1299/1309/0.53 | 1356/1370/0.56 | 5972/5991/4.30 | | DYHS+ | — | — | — | — | — | — | | | DYHS | — | — | — | — | — | — |
| | Algorithm | #26 (1000) | #27 (5000) | #28 (420) | #29 (110) | #30 (132) | #30 (462) |
| | | MDYHS+ | 1040/2080/0.63 | 24/24/0.036 | 1594/2930/2.94 | 256/372/0.14 | 416/699/0.24 | 2213/3889/4.16 | | MDYHS+1 | 1000/1000/0.46 | 24/24/0.036 | 3014/3034/3.89 | 280/286/0.12 | 318/333/0.15 | 1076/1097/1.51 | | DYHS+ | 390/720/0.22 | 38/282/0.22 | 1264/3001/2.39 | 229/479/0.14 | 413/906/0.27 | 1355/2925/2.53 | | | DYHS | 390/720/0.21 | 39/271/0.20 | 1485/3475/2.62 | 236/520/0.13 | 404/899/0.25 | 1415/2980/2.55 |
| | | MDYHS+ | 1289/2578/0.79 | 29/29/0.039 | 2364/4441/4.26 | 416/646/0.22 | 641/1149/0.41 | 3234/5894/6.22 | | MDYHS+1 | 1000/1000/0.48 | 29/29/0.039 | 5946/5966/7.64 | 1862/1895/0.83 | 554/569/0.26 | 2008/2029/2.80 | | DYHS+ | 8951/17009/5.20 | 49/358/0.24 | 3407/8062/6.28 | 394/835/0.25 | 800/1756/0.53 | 3353/7227/6.35 | | | DYHS | 6985/13160/3.81 | 48/330/0.22 | 3446/8045/6.30 | 447/961/0.26 | 781/1714/0.49 | 3499/7433/6.74 |
| | | MDYHS+ | 2072/4144/1.32 | 33/33/0.049 | 2873/5459/5.18 | 3470/5723/1.90 | 868/1603/0.57 | 4053/7532/7.97 | | MDYHS+1 | 1000/1000/0.50 | 33/33/0.051 | 8848/8868/11.38 | 2660/2693/1.19 | 794/809/0.38 | 2929/2950/4.10 | | DYHS+ | 20160/38721/11.86 | 57/413/0.28 | 6420/15036/11.67 | 2837/5939/1.66 | 1089/2365/0.79 | 5248/11260/10.04 | | | DYHS | 18349/35090/9.94 | 53/375/0.25 | 6067/14100/11.01 | 2857/5951/1.72 | 1165/2556/0.81 | 5641/12002/10.26 |
| | | MDYHS+ | 2931/5862/1.83 | 38/38/0.050 | 7543/12766/13.09 | 3681/6135/2.00 | 1276/2317/0.83 | 5300/9593/10.18 | | MDYHS+1 | 1003/1003/0.46 | 38/38/0.052 | 11287/11307/14.57 | 3370/3403/1.50 | 1039/1054/0.52 | 3858/3879/5.41 | | DYHS+ | 29056/55909/17.24 | 66/468/0.33 | 8118/19039/15.35 | 3651/7576/1.97 | 1461/3187/0.96 | 7351/15793/13.82 | | | DYHS | 27355/52663/14.61 | 67/459/0.32 | — | 3666/7598/2.14 | 1506/3316/0.98 | 7403/15795/14.09 |
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