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Regularization Methods for the Solution of Inverse Problems Theory and Computational Aspect

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10101010101010101010108−−− = sing. values x = rhs. coef. o = solution coef.20−2−4−6−8−10−1202468i1012141610

−2

GCV function, minimum at 0.000153

10

−4

10G(lambda)−6

10

−8

10

−10

10

−12

10

−14

10

−15

10

−10

10

−5

10

lambda

0

10

5

10

10

10

−2

GCV function, minimum at 0.0425

10

−3

10

−4

G(lambda)10

−5

10

−6

10

−7

10

−8

10−1510

−9

10

−10

10

−5

10

lambda

0

10

5

10

10

10

14

L−curve, Tikh. corner at 0.08466

9.108e−01410

12

10102.624e−012|| x || m10

8

ro7.56e−011n noitu10

6

los10

4

2.178e−0090.043236.275e−0081.808e−0060.000052080.00151.24510

2

10

0

10

0

10

1

102

10

3

104

10

5

residual norm || A x − b ||

GCV function, minimum at 0.6196105104103102)ad101bmal(G10010−110−210−310−410−1510−1010−51001051010lambda

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