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Theory and Modern Applications

Table 2 Discrete relative error estimations for the regularized solution at fixed values from y=0.6 to y=1.0

From: On a general filter regularization method for the 2D and 3D Poisson equation in physical geodesy

 

0.6

0.7

0.8

0.9

1.0

10−1

3.50E − 03

1.70E − 03

2.67E − 04

6.23E − 05

2.52E − 06

10−2

1.16E − 04

6.75E − 05

3.96E − 06

7.91E − 06

2.93E − 06

10−3

2.39E − 06

6.75E − 06

3.47E − 06

1.21E − 06

2.21E − 07

10−4

1.12E − 06

1.64E − 07

1.44E − 08

1.36E − 08

1.61E − 08

10−5

1.72E − 07

1.30E − 08

4.44E − 08

7.34E − 09

9.97E − 11

10−6

4.48E − 10

8.67E − 09

2.34E − 10

8.77E − 10

1.25E − 11

10−7

1.77E − 10

1.83E − 10

1.79E − 11

1.43E − 10

4.37E − 11

10−8

1.14E − 10

5.09E − 12

1.13E − 11

1.59E − 12

7.58E − 12

10−9

8.86E − 14

4.67E − 12

1.44E − 12

5.52E − 13

4.74E − 14

10−10

7.80E − 13

1.14E − 12

1.38E − 13

1.57E − 14

1.21E − 15