Research Article
Global Convergence of Schubert’s Method for Solving Sparse Nonlinear Equations
Table 1
Results of Algorithm
3 for Problems
1–
7.
| Pro | | | | | | Iter | Time (s) | | Iter | Time (s) |
| 1 | 50 | 26.8421 | 4.2686 − 06 | 17 | 0.0000 | 3.0281 − 06 | 12 | 0.0000 | 100 | 36.5103 | − 06 | 17 | 0.0000 | 3.0284 − 06 | 12 | 0.0000 | 200 | 50.5767 | 3.4126 − 06 | 19 | 0.0313 | 3.0284 − 06 | 12 | 0.0313 | 500 | 78.9494 | 3.5829 − 06 | 19 | 0.0313 | 3.0284 − 06 | 12 | 0.0313 | 1000 | 111.1665 | 6.7616 − 06 | 20 | 0.0938 | 3.0284 − 06 | 12 | 0.0625 | 3000 | 156.8247 | 4.6028 − 06 | 21 | 0.1780 | 3.0284 − 06 | 12 | 0.1563 | 5000 | 247.7055 | 5.0272 − 06 | 22 | 0.2063 | 3.0284 − 06 | 12 | 0.2031 | 10000 | 256.8910 | 5.6234 − 06 | 25 | 0.2028 | 3.0284 − 06 | 12 | 0.3125 | 20000 | 289.2351 | 5.4512 − 06 | 25 | 0.3276 | 3.0284 − 06 | 12 | 0.6563 |
| 2 | 50 | 6.9282 | 1.3431 − 06 | 10 | 0.0000 | 1.0235 − 06 | 4 | 0.0000 | 100 | 9.8995 | 1.8437 − 06 | 11 | 0.0000 | 1.0235 − 06 | 4 | 0.0000 | 200 | 14.0712 | 6.2185 − 06 | 11 | 0.0313 | 1.0235 − 06 | 4 | 0.0000 | 500 | 22.3159 | 2.6805 − 06 | 12 | 0.0313 | 1.0235 − 06 | 4 | 0.0000 | 1000 | 31.5911 | 7.8148 − 06 | 11 | 0.0625 | 1.0235 − 06 | 4 | 0.0313 | 3000 | 54.7540 | 8.5561 − 06 | 18 | 0.7188 | 1.0235 − 06 | 4 | 0.0625 | 5000 | 70.6965 | 8.3005 − 06 | 12 | 0.2500 | 1.0235 − 06 | 4 | 0.0938 | 10000 | 75.0126 | 8.2145 − 06 | 14 | 0.2808 | 1.0235 − 06 | 4 | 0.1406 | 20000 | 81.2659 | 8.5179 − 06 | 14 | 0.5304 | 1.0235 − 06 | 4 | 0.2500 |
| 3 | 50 | 8.5416 | 8.7650 − 08 | 3 | 0.0000 | 1.1795 − 07 | 5 | 0.0000 | 100 | 12.1562 | 6.8406 − 10 | 3 | 0.0000 | 5.3904 − 06 | 4 | 0.0000 | 200 | 17.2195 | 8.0105 − 06 | 2 | 0.0000 | 3.6741 − 07 | 3 | 0.0000 | 500 | 27.2392 | 3.3130 − 07 | 2 | 0.0000 | 1.2337 − 06 | 3 | 0.0000 | 1000 | 38.5246 | 2.9461 − 08 | 2 | 0.0000 | 1.5498 − 07 | 3 | 0.0313 | 3000 | 66.7279 | 6.3233 − 10 | 3 | 0.0313 | 3.0014 − 06 | 2 | 0.0313 | 5000 | 86.1455 | 1.0586 − 10 | 2 | 0.0313 | 1.0804 − 06 | 2 | 0.0625 | 10000 | 121.8282 | 9.3691 − 12 | 2 | 0.0938 | 2.7008 − 07 | 2 | 0.0938 | 20000 | 172.2911 | 8.7919 − 13 | 2 | 0.1563 | 6.7517 − 08 | 2 | 0.1719 |
| 4 | 50 | 0.1511 | 8.7479 − 06 | 19 | 0.0000 | 2.4065 − 06 | 13 | 0.0000 | 100 | 0.1111 | 8.4206 − 06 | 16 | 0.0000 | 5.7592 − 06 | 12 | 0.0000 | 200 | 0.0801 | 9.4752 − 06 | 18 | 0.0313 | 9.6492 − 06 | 10 | 0.0313 | 500 | 0.0512 | 8.2454 − 06 | 14 | 0.0313 | 9.0492 − 06 | 10 | 0.0313 | 1000 | 0.0364 | 7.7380 − 06 | 13 | 0.0625 | 4.0496 − 06 | 10 | 0.0625 | 3000 | 0.0211 | 7.6951 − 06 | 13 | 0.1719 | 9.7135 − 06 | 8 | 0.1250 | 5000 | 0.0163 | 9.8163 − 06 | 10 | 0.1875 | 8.4494 − 06 | 7 | 0.1563 | 10000 | 0.0115 | 8.4212 − 06 | 10 | 0.3125 | 4.1718 − 06 | 7 | 0.2344 | 20000 | 0.0082 | 6.9072 − 06 | 4 | 0.2656 | 2.0897 − 06 | 7 | 0.3906 |
| 5 | 50 | 0.0481 | 7.6492 − 06 | 9 | 0.0000 | 5.5212 − 06 | 9 | 0.0000 | 100 | 0.0315 | 5.3122 − 06 | 9 | 0.0000 | 9.8754 − 06 | 8 | 0.0000 | 200 | 0.0213 | 9.7441 − 06 | 8 | 0.0000 | 6.8642 − 06 | 8 | 0.0000 | 500 | 0.0131 | 6.1289 − 06 | 8 | 0.0000 | 4.2970 − 06 | 8 | 0.0000 | 1000 | 0.0092 | 4.3258 − 06 | 8 | 0.0000 | 7.9238 − 06 | 7 | 0.0000 | 3000 | 0.0053 | 6.5316 − 06 | 7 | 0.0000 | 4.5644 − 06 | 7 | 0.0000 | 5000 | 0.0041 | 5.0582 − 06 | 7 | 0.0000 | 9.2636 − 06 | 6 | 0.0000 | 10000 | 0.0029 | 9.3577 − 06 | 6 | 0.0000 | 6.5482 − 06 | 6 | 0.0313 | 20000 | 0.0020 | 6.6163 − 06 | 6 | 0.0313 | 4.6295 − 06 | 6 | 0.0313 |
| 6 | 50 | 0.0166 | 6.6166 − 06 | 7 | 0.0000 | 6.5364 − 06 | 5 | 0.0000 | 100 | 0.0116 | 7.5062 − 06 | 6 | 0.0000 | 8.5483 − 06 | 2 | 0.0000 | 200 | 0.0082 | 9.4436 − 06 | 4 | 0.0000 | 2.1372 − 06 | 2 | 0.0000 | 500 | 0.0052 | 9.8417 − 06 | 18 | 0.0406 | 5.2204 − 06 | 1 | 0.0000 | 1000 | 0.0037 | 9.6163 − 06 | 24 | 0.0313 | 3.6586 − 06 | 3 | 0.0313 | 3000 | 0.0021 | 8.3375 − 06 | 17 | 0.0625 | 2.1088 − 06 | 3 | 0.0313 | 5000 | 0.0016 | 9.7458 − 06 | 15 | 0.0938 | 1.6333 − 06 | 3 | 0.0313 | 10000 | 0.0012 | 9.9565 − 06 | 11 | 0.1563 | 1.1548 − 06 | 3 | 0.0313 | 20000 | 0.0082 | 8.8706 − 06 | 9 | 0.2031 | 8.1653 − 06 | 2 | 0.0625 |
| 7 | 50 | 0.2271 | 1.4914 − 14 | 2 | 0.0000 | 5.9494 − 06 | 53 | 0.1250 | 100 | 0.2319 | 1.4792 − 14 | 2 | 0.0000 | 5.6147 − 06 | 58 | 0.0938 | 200 | 0.2413 | 1.4960 − 14 | 2 | 0.0000 | 6.6486 − 06 | 77 | 0.2031 | 500 | 0.2675 | 1.5760 − 14 | 2 | 0.0000 | 7.4199 − 06 | 70 | 0.7500 | 1000 | 0.3062 | 0 | 2 | 0.0313 | 8.2082 − 06 | 35 | 0.3906 | 3000 | 0.4274 | 0 | 4 | 0.0625 | 5.7188 − 06 | 53 | 10.5469 | 5000 | 0.5211 | 0 | 7 | 2.5000 | 6.7092 − 06 | 41 | 19.0625 | 10000 | 0.7027 | 0 | 9 | 10.3125 | 6.8420 − 06 | 45 | 25.0156 | 20000 | 0.9686 | 0 | 11 | 43.7500 | 7.1086 − 06 | 51 | 30.0156 |
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