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