A Modified Spectral PRP Conjugate Gradient Projection Method for Solving Large-Scale Monotone Equations and Its Application in Compressed Sensing

Table 1

Numerical performance with fixed initial points.

Problem	Dim	Method	CPU-time	Ni	Nf
P1	10000	MPPRP-M	0.049106	19	60
		MPPRP-W	0.083986	28	132
		MSDFPB	0.207396	49	357
		PRP	0.210513	57	373
		MPRP	0.225433	49	357
		TPRP	0.205193	49	357
		DFPB1	0.208191	52	360
		DFPB2	0.180871	41	333
		MHS	0.201207	49	357
P1	20000	MPPRP-M	0.097751	20	63
		MPPRP-W	0.202214	34	187
		MSDFPB	0.538910	63	522
		PRP	0.601340	72	544
		MPRP	0.578528	63	522
		TPRP	0.567042	63	522
		DFPB1	0.564317	67	534
		DFPB2	0.538403	56	503
		MHS	0.568248	63	522
P1	50000	MPPRP-M	0.189582	20	63
		MPPRP-W	0.776513	47	317
		MSDFPB	2.349394	93	913
		PRP	2.426823	101	926
		MPRP	2.373229	93	913
		TPRP	2.32399	93	913
		DFPB1	2.421556	97	925
		DFPB2	2.364173	86	894
		MHS	2.601235	93	913
P1	100000	MPPRP-M	0.519087	21	66
		MPPRP-W	2.762991	61	478
		MSDFPB	9.002493	127	1384
		PRP	9.108308	135	1402
		MPRP	9.448788	127	1384
		TPRP	8.986777	127	1384
		DFPB1	9.100524	130	1391
		DFPB2	8.819755	119	1360
		MHS	9.419715	127	1384
P2	10000	MPPRP-M	0.054535	19	60
		MPPRP-W	0.088811	28	132
		MSDFPB	0.217590	49	357
		PRP	0.218645	57	373
		MPRP	0.226537	49	357
		TPRP	0.226429	49	357
		DFPB1	0.210470	52	360
		DFPB2	0.204578	41	333
		MHS	0.234442	49	357
P2	20000	MPPRP-M	0.089917	20	63
		MPPRP-W	0.198822	34	187
		MSDFPB	0.563358	63	522
		PRP	0.604772	72	544
		MPRP	0.670294	63	522
		TPRP	0.677819	63	522
		DFPB1	0.679165	67	534
		DFPB2	0.607357	56	503
		MHS	0.589872	63	522
P2	50000	MPPRP-M	0.191132	20	63
		MPPRP-W	0.720108	47	317
		MSDFPB	2.248779	93	913
		PRP	2.464597	101	926
		MPRP	2.353173	93	913
		TPRP	2.342777	93	913
		DFPB1	2.363392	97	925
		DFPB2	2.279782	86	894
		MHS	2.384060	93	913
P2	100000	MPPRP-M	0.516081	21	66
		MPPRP-W	2.734834	61	478
		MSDFPB	9.004299	127	1384
		PRP	8.763470	135	1402
		MPRP	8.647855	127	1384
		TPRP	8.626593	127	1384
		DFPB1	8.626593	130	1391
		DFPB2	8.476836	119	1360
		MHS	8.905454	127	1384
P3	5000	MPPRP-M	0.077881	22	69
		MPPRP-W	0.955814	127	1360
		MSDFPB	2.155000	242	3141
		PRP	2.346950	251	3167
		MPRP	2.200878	242	3141
		TPRP	2.204338	242	3141
		DFPB1	2.246450	245	3148
		DFPB2	2.209059	234	3117
		MHS	2.236389	242	3141
P3	10000	MPPRP-M	0.145481	23	72
		MPPRP-W	2.590862	174	2059
		MSDFPB	6.749566	337	4751
		PRP	6.892930	346	4767
		MPRP	6.843273	337	4751
		TPRP	6.885266	337	4751
		DFPB1	7.222119	341	4763
		DFPB2	6.881919	330	4732
		MHS	6.992060	337	4751
P3	15000	MPPRP-M	0.190225	23	72
		MPPRP-W	4.894470	212	2656
		MSDFPB	12.242514	411	6059
		PRP	13.494894	420	6078
		MPRP	13.547676	411	6059
		TPRP	12.255626	411	6059
		DFPB1	12.473808	415	6071
		DFPB2	12.734751	404	6040
		MHS	12.425026	411	6059
P3	20000	MPPRP-M	0.239615	23	72
		MPPRP-W	7.505229	242	3126
		MSDFPB	18.305460	472	7144
		PRP	19.195911	481	7169
		MPRP	19.482789	472	7144
		TPRP	19.011112	472	7144
		DFPB1	19.165800	475	7151
		DFPB2	19.428512	464	7120
		MHS	18.928398	472	7144
P4	10000	MPPRP-M	0.061549	16	102
		MPPRP-W	0.113153	19	131
		MSDFPB	0.289696	68	555
		PRP	0.187397	39	391
		MPRP	0.233670	48	462
		TPRP	0.358863	89	658
		DFPB1	0.657537	185	1142
		DFPB2	0.213256	40	422
		MHS	0.414446	62	803
P4	20000	MPPRP-M	0.125760	17	108
		MPPRP-W	0.256772	31	203
		MSDFPB	0.703061	79	730
		PRP	0.558050	52	565
		MPRP	0.663444	59	635
		TPRP	0.822848	100	833
		DFPB1	1.442003	203	1352
		DFPB2	0.565771	51	596
		MHS	0.674281	60	724
P4	50000	MPPRP-M	0.295365	17	108
		MPPRP-W	0.961757	38	273
		MSDFPB	2.972641	102	1109
		PRP	2.655601	73	943
		MPRP	2.738925	81	1007
		TPRP	3.209823	122	1207
		DFPB1	4.783178	234	1771
		DFPB2	2.644189	75	981
		MHS	6.106110	158	2717
P4	100000	MPPRP-M	0.768978	17	108
		MPPRP-W	3.113887	45	357
		MSDFPB	10.575505	129	1568
		PRP	9.164701	101	1406
		MPRP	9.756561	108	1465
		TPRP	11.151034	146	1651
		DFPB1	16.812871	275	2301
		DFPB2	9.292510	99	1423
		MHS	21.792651	179	3305
P5	100	MPPRP-M	0.012253	18	77
		MPPRP-W	0.018540	62	555
		MSDFPB	0.049702	129	1522
		PRP	0.033290	144	1558
		MPRP	0.033017	139	1560
		TPRP	0.034758	128	1518
		DFPB1	0.026313	150	1601
		DFPB2	0.029466	131	1538
		MHS	0.040165	133	1539
P5	500	MPPRP-M	0.016447	22	93
		MPPRP-W	0.231399	544	9066
		MSDFPB	0.772128	1313	25232
		PRP	0.727796	1332	25274
		MPRP	0.585951	1372	25394
		TPRP	0.577368	1315	25238
		DFPB1	0.578794	1337	25315
		DFPB2	0.589438	1317	25247
		MHS	0.595316	1315	25241
P5	1000	MPPRP-M	0.017438	23	97
		MPPRP-W	1.072332	1505	29740
		MSDFPB	3.218997	3680	81797
		PRP	2.889154	3696	81825
		MPRP	2.963704	3735	81946
		TPRP	2.948045	3682	81802
		DFPB1	3.040253	3704	81880
		DFPB2	3.045603	3683	81803
		MHS	3.220028	3678	81791
P5	2000	MPPRP-M	0.021613	25	106
		MPPRP-W	5.944706	4206	95732
		MSDFPB	17.227153	10341	260347
		PRP	16.073363	10355	260379
		MPRP	16.960973	10394	260490
		TPRP	16.826907	10343	260352
		DFPB1	16.257104	10364	260424
		DFPB2	16.739385	10345	260356
		MHS	17.503252	10339	260342
P6	100	MPPRP-M	0.217224	1182	3717
		MPPRP-W	0.193153	1148	3605
		MSDFPB	0.237793	1186	3706
		PRP	0.220389	1207	3766
		MPRP	0.224211	1186	3658
		TPRP	0.248104	1195	3722
		DFPB1	0.236804	1201	3750
		DFPB2	0.235470	1170	3620
		MHS	0.236250	1198	3720
P6	500	MPPRP-M	0.944828	1348	5050
		MPPRP-W	0.794555	1278	4482
		MSDFPB	0.797832	1185	3968
		PRP	0.911934	1322	4267
		MPRP	0.845336	1258	3983
		TPRP	0.912343	1326	4335
		DFPB1	0.903852	1321	4300
		DFPB2	1.020228	1299	4143
		MHS	0.918611	1307	4147
P6	1000	MPPRP-M	2.337405	1495	6667
		MPPRP-W	1.680275	1381	4951
		MSDFPB	1.536904	1331	4320
		PRP	1.851282	1389	4553
		MPRP	1.647356	1277	4040
		TPRP	1.686418	1273	4109
		DFPB1	1.792886	1360	4409
		DFPB2	1.812678	1343	4330
		MHS	1.775351	1341	4283
P6	2000	MPPRP-M	6.738143	1737	11016
		MPPRP-W	3.257538	1440	4936
		MSDFPB	3.065903	1381	4524
		PRP	3.574894	1390	4522
		MPRP	3.381889	1316	4247
		TPRP	3.565741	1378	4510
		DFPB1	3.609619	1377	4511
		DFPB2	3.647662	984	3232
		MHS	3.608315	1362	4397