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Table 1 Numerical results

From: A quasi-Newton algorithm for large-scale nonlinear equations

  

New method with CG

Normal method (only main algorithm)

P

Dim

NI/NG

GF

GD

cpu time

NI/NG

GF

GD

cpu time

1

1000

1/1

6.676674e−006

1.335335e−005

0.000000e+000

0/2

6.676674e−006

1.335335e−005

0.000000e+000

2000

1/1

3.335834e−006

6.671668e−006

0.000000e+000

0/2

3.335834e−006

6.671668e−006

0.000000e+000

3000

1/1

2.223334e−006

4.446667e−006

1.560010e−002

0/2

2.223334e−006

4.446667e−006

3.120020e−002

2

1000

12/17

1.570352e−007

1.214954e−007

1.544410e+000

199/2879

1.624268e−004

1.228551e+000

1.338801e+002

2000

200/2927

8.144022e−005

3.138945e−001

8.647135e+002

199/2928

8.144022e−005

3.138945e−001

8.680832e+002

3000

200/2326

5.434381e−005

2.481121e−003

1.614626e+003

199/2327

5.434381e−005

2.481121e−003

1.622785e+003

3

1000

8/8

4.194859e−006

8.389718e−006

1.560010e−002

115/1009

5.838535e−008

1.171251e−007

7.996611e+001

2000

8/8

7.775106e−006

1.555021e−005

7.800050e−002

117/1040

1.161670e−007

2.328056e−007

5.662368e+002

3000

9/9

1.614597e−012

3.231630e−012

1.553770e+001

137/1362

1.739498e−007

3.484891e−007

2.141410e+003

4

1000

92/165

5.632576e−006

5.669442e−006

2.215214e+000

199/285

3.703283e+001

1.196051e+001

1.356897e+002

2000

87/156

6.245922e−006

6.085043e−006

1.502290e+001

199/230

3.637504e+000

9.570779e+000

9.591097e+002

3000

94/169

6.678153e−006

6.437585e−006

4.731510e+001

199/234

2.639260e+002

1.904865e+001

3.096277e+003

5

1000

22/51

8.288299e−006

6.268946e−007

2.106014e+000

199/2570

3.195300e+004

4.649782e+006

1.779971e+001

2000

21/50

4.114462e−006

1.943351e−006

5.179233e+000

199/2652

6.395300e+004

1.354972e+005

8.327333e+001

3000

21/51

9.843373e−006

8.504719e−006

1.597450e+001

199/2853

9.595300e+004

1.135356e+005

1.314776e+002

6

1000

9/11

5.984185e−012

1.197596e−011

7.176046e−001

6/9

6.069722e−007

1.118437e−006

4.149627e+000

2000

9/11

1.505191e−006

3.010383e−006

7.800050e−002

6/9

1.210931e−006

2.231765e−006

2.898499e+001

3000

9/11

2.251571e−006

4.503142e−006

1.404009e−001

6/9

1.814891e−006

3.345093e−006

9.300780e+001

7

1000

200/602

1.208240e−003

4.697005e+000

3.424222e+001

199/573

3.156137e+005

3.893380e+004

1.378113e+002

2000

200/760

1.612671e+001

9.034319e+000

2.420200e+002

199/644

1.014481e+006

3.131576e+005

9.872367e+002

3000

200/693

5.570227e−003

9.501149e+001

7.698181e+002

199/743

9.357473e+007

2.087488e+007

3.087119e+003

8

1000

2/2

0.000000e+000

0.000000e+000

0.000000e+000

1/3

0.000000e+000

0.000000e+000

6.552042e−001

2000

2/2

0.000000e+000

0.000000e+000

0.000000e+000

1/3

0.000000e+000

0.000000e+000

4.820431e+000

3000

2/2

0.000000e+000

0.000000e+000

6.240040e−002

1/3

0.000000e+000

0.000000e+000

1.538170e+001

9

1000

67/118

7.138941e−006

1.820053e−005

3.010819e+000

2/5

2.358640e−006

4.611203e−006

1.404009e+000

2000

70/124

6.342724e−006

1.607326e−005

2.062333e+001

2/5

5.917002e−007

1.169969e−006

9.703262e+000

3000

74/131

7.447187e−006

1.799920e−005

6.450641e+001

2/5

2.632811e−007

5.225655e−007

3.084140e+001

10

1000

26/49

2.044717e−008

3.900140e−008

2.359983e+002

121/125

7.382123e−006

1.467673e−005

4.987196e+002

2000

24/47

9.030382e−006

2.717060e−006

1.847286e+003

121/125

7.454090e−006

1.481981e−005

3.852538e+003

3000

27/51

6.468831e−009

1.138377e−008

6.632227e+003

121/125

7.523322e−006

1.495745e−005

1.299774e+004