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Theory and Modern Applications

Table 2 Numerical results for different ε under an a posteriori choice rule for three regularization methods about Examples 2

From: A posteriori truncated regularization method for identifying unknown heat source on a spherical symmetric domain

 

ε

0.05

0.01

0.005

0.001

0.0005

0.0001

Truncate

\(e_{a}\)

0.0972

0.0521

0.0304

0.0241

0.0226

0.0139

\(e_{r}\)

0.2392

0.1283

0.0749

0.0594

0.0557

0.0341

Tikhonov

\(e_{a}\)

0.1295

0.0871

0.0361

0.0273

0.0243

0.0378

\(e_{r}\)

0.3178

0.2143

0.0889

0.0672

0.0598

0.0930

Quasi-boundary

\(e_{a}\)

0.7800

0.2036

0.0566

0.0539

0.0482

0.0393

\(e_{r}\)

1.9194

0.5011

0.1393

0.1327

0.1186

0.0967