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Table 2 ITs and CPUs of SOR-like, MSOR-like [15], NSOR-like [14], GNSOR-like, and NSSOR-like for Example 4.1

From: Some generalizations of the new SOR-like method for solving symmetric saddle-point problems

m 128 512 1152 2048 8192
n 64 256 576 1024 4096
m + n 192 768 1728 3072 12,288
Case I SOR-like \(\omega_{\exp }\) 0.4644 0.2720 0.1886 0.1386 0.0741
IT 73 202 221 315 657
CPU 0.0284 0.1321 0.3670 0.9262 9.0859
MSOR-like [15] \(\alpha_{\exp}\) 1.7212 1.8256 1.8737 1.9136 1.9201
\(\omega_{\exp}\) 0.3159 0.1873 0.1328 0.1020 0.0541
IT 67 140 183 223 462
CPU 0.0313 0.1171 0.2937 0.6137 6.3687
NSOR-like [14] \(\alpha_{\exp}\) 1.7212 1.8256 1.8689 1.9699 1.9219
\(\beta_{\exp}\) 0.3700 0.3655 0.3492 0.2399 0.2148
\(\omega_{\exp}\) 0.3159 0.1873 0.1328 0.1001 0.0545
IT 55 105 160 212 457
CPU 0.0250 0.1031 0.2624 0.5687 6.2634
GNSOR-like \(\alpha_{\exp}\) 1.7212 1.8256 1.8689 1.9699 1.9219
\(\beta_{\exp}\) 0.3700 0.3655 0.3492 0.2399 0.2148
\(\omega_{\exp}\) 0.3250 0.1923 0.1361 0.1029 0.0555
\(\tau_{\exp}\) 0.3130 0.1830 0.1282 0.0985 0.0534
IT 50 101 155 211 447
CPU 0.0154 0.1019 0.2561 0.5663 6.1488
Case II SOR-like \(\omega_{\exp }\) 0.5958 0.3657 0.2215 0.1961 0.0945
IT 56 103 183 216 509
CPU 0.0310 0.1343 0.5855 1.4298 16.1417
MSOR-like [15] \(\alpha_{\exp}\) 1.6599 1.7732 1.8315 1.8753 1.9200
\(\omega_{\exp}\) 0.3996 0.2498 0.1806 0.1257 0.0745
IT 45 94 167 175 330
CPU 0.0306 0.1194 0.6196 1.2068 10.4589
NSOR-like [14] \(\alpha_{\exp}\) 1.6469 1.7582 1.8318 1.8750 1.9100
\(\beta_{\exp}\) 0.3397 0.3438 0.3640 0.3541 0.4001
\(\omega_{\exp}\) 0.3986 0.2513 0.1812 0.1420 0.0758
IT 39 77 116 155 320
CPU 0.0164 0.0916 0.4162 1.0173 9.4823
GNSOR-like \(\alpha_{\exp}\) 1.6469 1.7582 1.8318 1.8750 1.9100
\(\beta_{\exp}\) 0.3397 0.3438 0.3640 0.3541 0.4001
\(\omega_{\exp}\) 0.4030 0.2513 0.1825 0.1402 0.0758
\(\tau_{\exp}\) 0.4210 0.2581 0.1823 0.1443 0.0755
IT 37 75 115 154 319
CPU 0.0134 0.0871 0.3219 1.0129 9.4803