Skip to main content

Table 3 Numerical results

From: A conjugate gradient algorithm and its application in large-scale optimization problems and image restoration

NO

Dim

Algorithm 2.1

Algorithm 1

NI

NFG

CPU

NI

NFG

CPU

1

30,000

572

2832

17.170120

575

2844

17.689130

2

30,000

217

1082

10.122250

63

312

2.980625

3

30,000

43

170

0.886250

47

186

0.995250

4

30,000

1014

4385

23.856440

2007

8265

44.962060

5

30,000

312

1145

1.994063

5204

20,616

32.667130

6

30,000

623

3084

13.556880

607

3004

15.491130

7

30,000

195

584

1.625188

195

584

2.082937

8

30,000

114

567

2.542562

114

567

3.302094

9

30,000

78

297

0.970500

1799

3598

16.080500

10

30,000

276

1100

3.950344

256

1020

3.633312

11

30,000

116

448

3.119172

46

137

0.968500

12

30,000

214

640

2.761031

835

2460

10.498130

13

30,000

5

16

0.093313

78

233

1.184125

14

30,000

4909

19,634

285.120600

1464

5821

83.039530

15

30,000

551

2201

7.004469

1430

4822

15.256470

16

30,000

4

8

0.078563

4

8

0.061656

17

30,000

3916

15,660

56.706440

3725

14,896

53.351160

18

30,000

570

2260

45.941410

649

2496

50.545590

19

30,000

539

2096

22.635000

606

2297

25.423720

20

30,000

1485

5904

16.661230

1201

4573

13.690940

21

30,000

12

37

0.187125

424

1271

7.530531

22

30,000

54

214

0.796953

54

214

0.811281

23

30,000

7833

15,670

89.310080

7796

15,596

90.177780

24

30,000

747

3698

14.320530

2989

14,796

57.666090

25

30,000

828

3854

27.081220

1271

5619

40.056130

26

30,000

1088

5415

17.331190

24

114

0.383531

27

30,000

10,000

49,997

46.690160

3638

18,022

9.802813

28

30,000

766

3772

12.792700

766

3772

13.070120

29

30,000

890

4381

23.664730

890

4381

24.005910

30

30,000

1287

6398

38.251670

3898

19,316

118.245100

31

30,000

24

94

0.155719

24

94

0.151094

32

30,000

26

77

0.249469

26

77

0.251750

33

30,000

1470

7328

25.383470

3749

18,573

65.219060

34

30,000

80

397

4.352656

80

397

4.436313

35

30,000

723

3607

20.137970

1370

5627

34.018590

36

30,000

10,000

39,998

344.076300

4452

17,604

153.518100

37

30,000

98

486

1.090125

98

486

1.215531

38

30,000

666

2246

22.198280

651

2198

21.966780

39

30,000

2

7

0.062063

2

7

0.064031

40

30,000

2880

14,397

115.767600

2879

14,392

117.060600

41

30,000

510

1795

17.488940

546

1846

18.727130

42

30,000

34

135

0.125313

689

2707

2.399625

43

30,000

5492

27,391

15.740310

3729

18,476

10.305280

44

30,000

6489

32,372

123.601100

4540

22,492

81.385600

45

30,000

527

2092

20.201500

535

2115

20.517880

46

30,000

167

502

1.542719

1664

4911

15.354250

47

30,000

24

117

0.717750

24

117

0.716781

48

30,000

893

2678

5.958000

893

2678

6.079031

49

30,000

65

215

0.265969

646

1909

2.798000

50

30,000

2

7

0.062344

2

7

0.065219

51

30,000

1308

6537

52.088220

1310

6547

53.276810

52

30,000

7764

38,817

331.998400

7765

38,822

336.152700

53

30,000

509

1793

17.501380

539

1827

18.521470

54

30,000

2

7

0.064375

2

7

0.066031

55

30,000

2059

10,292

85.489190

2061

10,302

89.237690

56

30,000

1088

4350

3.479906

1088

4350

3.700406

57

30,000

2

6

0.014438

2

6

0.002281

58

30,000

19

56

0.295813

34

100

0.518375

59

30,000

501

1502

8.905937

501

1502

9.458844

60

30,000

962

3918

45.193690

1033

4129

49.081910

61

30,000

2

7

0.060375

2

7

0.062875

62

30,000

65

215

0.266781

646

1909

2.940375

63

30,000

1

215

5.836156

1

1909

5.956969

64

30,000

10,000

49,846

26.754220

7151

35,419

19.496940

65

30,000

10,000

49,863

26.738310

4461

22,096

12.329940

1

90,000

573

2836

51.941500

575

2844

52.787310

2

90,000

30

147

4.165094

5

22

0.633250

3

90,000

44

174

2.746031

47

186

3.082438

4

90,000

1551

6524

107.156900

2007

8265

137.040400

5

90,000

722

2796

15.007690

5626

22,298

114.106400

6

90,000

338

1687

23.915000

339

1692

24.350190

7

90,000

195

584

4.992938

195

584

5.162625

8

90,000

13

31

0.354344

2805

5610

68.010120

9

90,000

241

961

10.348970

226

901

9.954906

10

90,000

39

151

3.215312

46

137

3.037875

11

90,000

215

643

8.439844

1118

3291

44.010810

12

90,000

5

16

0.248438

78

233

3.493094

13

90,000

5188

20,750

909.355400

1498

5955

268.589000

14

90,000

854

3388

33.367970

1485

4987

50.862160

15

90,000

4

8

0.203781

4

8

0.201875

16

90,000

4097

16,384

181.834700

3938

15,748

178.470700

17

90,000

577

2282

139.602700

651

2501

151.183100

18

90,000

540

2099

68.454150

606

2297

76.485500

19

90,000

1912

7602

66.348030

1201

4573

42.566220

20

90,000

35

108

1.810375

450

1349

24.126810

21

90,000

54

214

2.466781

54

214

2.486906

22

90,000

7833

15,670

274.592900

7796

15,596

283.996600

23

90,000

93

460

5.444188

1085

5312

66.299620

24

90,000

961

4387

93.333880

1271

5619

120.455800

25

90,000

1088

5415

53.056840

24

114

1.183812

26

90,000

2051

10180

20.263250

3731

18,486

35.322310

27

90,000

748

3701

38.751530

748

3701

39.540090

28

90,000

891

4387

71.637530

891

4387

72.518130

29

90,000

1284

6402

105.456800

3898

19,320

332.476700

30

90,000

24

94

0.467781

24

94

0.483219

31

90,000

26

77

0.779031

26

77

0.777844

32

90,000

1133

5635

59.076220

3249

16,242

190.573400

33

90,000

24

117

3.867094

24

117

3.884219

34

90,000

714

3565

60.103160

1650

7029

125.869400

35

90,000

10,000

39,998

1042.793000

4473

17,688

463.743300

36

90,000

60

297

2.058625

60

297

2.087188

37

90,000

694

2330

69.748030

677

2276

68.414340

38

90,000

2

7

0.204938

2

7

0.195375

39

90,000

2880

14,397

350.003800

2879

14,392

352.487200

40

90,000

491

1737

51.027900

622

2060

63.507870

41

90,000

54

215

0.649813

693

2719

8.442843

42

90,000

1169

5823

11.180380

3730

18,481

35.198530

43

90,000

1167

5808

64.462680

4541

22,497

315.836300

44

90,000

529

2098

61.044750

535

2115

61.438470

45

90,000

222

665

6.377344

1588

4688

45.179410

46

90,000

8

37

0.669438

8

37

0.678719

47

90,000

948

2843

19.813470

948

2843

20.081030

48

90,000

65

215

0.858969

646

1909

7.911000

49

90,000

2

7

0.202594

2

7

0.196938

50

90,000

1308

6537

160.226500

1310

6547

159.038700

51

90,000

7765

38,822

1003.051000

7765

38,822

1012.967000

52

90,000

498

1761

51.683120

608

2018

62.156810

53

90,000

2

7

0.202531

2

7

0.199563

54

90,000

7434

37,167

930.166400

7434

37,167

938.409400

55

90,000

2059

10,292

258.693500

2062

10,307

262.954400

56

90,000

1088

4350

11.823500

1088

4350

12.275250

57

90,000

2

6

0.014281

2

6

0.017813

58

90,000

23

68

1.075656

34

100

1.572375

59

90,000

528

1583

28.627440

528

1583

28.943250

60

90,000

1039

4153

144.438500

1088

4349

151.380900

61

90,000

2

7

0.188031

2

7

0.192125

62

90,000

65

215

0.843531

646

1909

7.941813

63

90,000

1

215

52.368780

1

1909

52.762500

64

90,000

10,000

49,830

90.154590

7332

36,324

69.138880

65

90,000

9386

46,763

84.491620

4622

22,904

44.597250

1

150,000

573

2836

86.975000

575

2844

87.901440

2

150,000

8

37

1.761812

22

107

5.196187

3

150,000

44

174

4.586094

47

186

4.939875

4

150,000

1849

7707

211.646100

2007

8265

228.498600

5

150,000

791

3071

28.159620

6042

23,961

204.553600

6

150,000

1193

5950

109.430100

3752

18,593

340.449900

7

150,000

243

1212

28.998030

244

1217

29.267750

8

150,000

195

584

8.379937

195

584

8.431313

9

150,000

12

28

0.549281

3396

6792

140.188300

10

150,000

182

725

13.544060

178

709

13.124880

11

150,000

33

122

4.384094

46

137

4.963875

12

150,000

185

553

12.357280

1304

3837

85.495120

13

150,000

5

15

0.375813

78

233

5.665125

14

150,000

5317

21,266

1558.335000

1518

6035

435.598100

15

150,000

652

2597

43.007870

1510

5062

83.542500

16

150,000

4

8

0.327438

4

8

0.331625

17

150,000

4185

16,736

310.876300

4038

16,148

302.085700

18

150,000

577

2282

234.017300

651

2501

250.321700

19

150,000

543

2108

115.348700

606

2297

126.085400

20

150,000

1856

7388

108.733000

1201

4573

69.361500

21

150,000

37

114

3.196656

462

1385

41.271310

22

150,000

54

214

4.151344

54

214

4.162875

23

150,000

7833

15,670

463.476000

7796

15,596

470.208800

24

150,000

70

347

6.909438

697

3370

67.468870

25

150,000

911

4185

149.822700

1271

5619

200.791100

26

150,000

1088

5415

89.901440

24

114

1.983250

27

150,000

2215

11,021

35.738090

3730

18,481

62.137870

28

150,000

741

3672

64.568810

741

3672

65.072250

29

150,000

889

4377

121.323800

889

4377

121.201100

30

150,000

981

4890

125.251900

3772

18,694

85,912.53

31

150,000

24

94

0.809406

24

94

0.824999

32

150,000

26

77

1.310812

26

77

1.307996

33

150,000

14

67

3.713187

14

67

3.747922

34

150,000

703

3511

100.417200

1388

6145

186.073000

35

150,000

10,000

39,998

1754.543000

4503

17,809

787.514800

36

150,000

38

187

2.184250

38

187

2.263187

37

150,000

707

2369

118.873700

690

2315

118.594500

38

150,000

2

7

0.325656

2

7

0.332813

39

150,000

2880

14,397

587.451400

2879

14,392

606.360800

40

150,000

10,000

30,267

1747.903000

672

2196

113.973500

41

150,000

184

735

3.663625

694

2722

13.838310

42

150,000

1358

6771

22.041560

3702

18,337

202.568000

43

150,000

1210

6037

111.168500

4543

22,507

1077.162000

44

150,000

530

2101

102.349000

535

2115

109.978700

45

150,000

274

819

13.210880

1690

4988

98.434780

46

150,000

7

32

0.966938

7

32

1.057281

47

150,000

973

2918

34.427190

973

2918

38.767780

48

150,000

65

215

1.448500

646

1909

15.874250

49

150,000

2

7

0.331188

2

7

0.354250

50

150,000

1308

6537

263.783100

1311

6552

293.491800

51

150,000

7765

38,822

1684.177000

7766

38,827

1981.202000

52

150,000

10,000

30,268

1756.903000

644

2118

119.279600

53

150,000

2

7

0.324875

2

7

0.425313

54

150,000

7434

37,167

1561.060000

7434

37,167

1800.328000

55

150,000

2059

10,292

446.907300

2062

10,307

487.069700

56

150,000

1088

4350

20.671000

1088

4350

25.482500

57

150,000

2

6

0.030125

2

6

0.043125

58

150,000

28

83

2.166875

34

100

2.942250

59

150,000

540

1619

49.252810

541

1622

54.262940

60

150,000

1086

4341

253.299800

1114

4453

281.304400

61

150,000

2

7

0.314938

2

7

0.324813

62

150,000

65

215

1.469437

646

1909

15.412690

63

150,000

1

215

145.548700

1

1909

159.423600

64

150,000

10,000

49,809

196.063200

7233

35,833

189.318800

65

150,000

8676

43,204

140.774700

4592

22,753

93.901630

1

210,000

573

2836

122.895800

575

2844

123.117700

2

210,000

53

262

17.625310

56

277

19.078840

3

210,000

44

174

6.490313

47

186

6.942719

4

210,000

2053

8524

329.735100

2007

8265

363.818300

5

210,000

839

3263

42.105750

6047

23,976

318.768000

6

210,000

1385

6911

176.616000

3778

18,725

481.052400

7

210,000

195

972

32.574000

196

977

32.512590

8

210,000

195

584

11.812690

195

584

11.700880

9

210,000

10

25

0.636500

3828

7656

216.963400

10

210,000

151

601

15.601060

149

593

16.178340

11

210,000

35

133

7.425500

46

137

6.971656

12

210,000

159

475

14.729620

1457

4286

133.270000

13

210,000

7

21

0.690063

78

233

7.877844

14

210,000

5403

21,610

2218.623000

1531

6085

613.377000

15

210,000

1027

4086

95.329560

1527

5113

117.547900

16

210,000

4

8

0.469438

4

8

0.469063

17

210,000

4244

16,972

440.685700

4103

16,408

427.691300

18

210,000

578

2286

327.911200

651

2501

349.330900

19

210,000

543

2108

161.378500

606

2297

11,790.320000

20

210,000

2097

8332

171.760500

1201

4573

97.047560

21

210,000

41

129

5.103688

470

1409

58.391690

22

210,000

54

214

5.743125

54

214

5.820063

23

210,000

7833

15,670

654.266300

7796

15,596

652.518700

24

210,000

400

1997

55.551690

1261

6156

171.682500

25

210,000

1088

5415

125.671300

24

114

2.806562

26

210,000

2035

10,133

46.097440

3732

18,491

107.095900

27

210,000

686

3427

84.321690

686

3427

85.084120

28

210,000

872

4292

163.879400

872

4292

163.689200

29

210,000

1207

6011

219.317600

4992

24,796

874.306100

30

210,000

24

94

1.136250

24

94

1.203375

31

210,000

26

77

1.813437

26

77

1.918250

32

210,000

10

47

3.683844

10

47

3.776062

33

210,000

638

3187

127.252500

641

3202

127.119400

34

210,000

28

137

2.273625

28

137

2.449063

35

210,000

715

2393

169.418200

698

2339

164.307800

36

210,000

2

7

0.448313

2

7

0.455063

37

210,000

2880

14,397

825.603000

2879

14,392

829.216300

38

210,000

283

1131

7.781998

695

2725

20.372810

39

210,000

1240

6188

28.252000

3597

17,819

209.757800

40

210,000

1128

5627

145.184000

4559

22,590

1239.831000

41

210,000

371

1109

25.005980

1735

5125

127.223700

42

210,000

20

97

4.087996

19

92

4.170031

43

210,000

990

2969

49.404980

990

2969

49.341160

44

210,000

65

215

2.028015

646

1909

19.142310

45

210,000

2

7

0.452000

2

7

0.453688

46

210,000

1308

6537

368.925000

1311

6552

458.029900

47

210,000

7765

38,822

2364.621000

7766

38,827

3018.524000

48

210,000

10,000

30,268

2460.779000

676

2206

166.936300

49

210,000

2

7

0.467848

2

7

0.466844

50

210,000

7434

37,167

2191.087000

7434

37,167

3023.795000

51

210,000

2059

10,292

608.572100

2062

10,307

653.233600

52

210,000

1088

4350

28.642380

1088

4350

38.929310

53

210,000

2

6

0.030805

2

6

0.047719

54

210,000

34

102

3.696555

34

100

4.255938

55

210,000

548

1643

69.857270

549

1646

78.052220

56

210,000

1106

4421

360.469800

1130

4517

1023.525000

57

210,000

2

7

0.453117

2

7

0.492094

58

210,000

65

215

2.011992

646

1909

21.231910

59

210,000

1

215

285.122300

1

1909

318.237500

60

210,000

10,000

49,791

317.897200

7278

36,056

876.884300

61

210,000

8113

40,386

201.801700

4592

22,753

227.298400