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Table 1 Error estimate between the exact solution and its regularized solution for the a priori parameter and the a posteriori parameter choice rules in Example 1

From: On an inverse problem in the parabolic equation arising from groundwater pollution problem

ϵ \(\boldsymbol{E_{1}^{\mu_{1}}}\) \(\boldsymbol{E_{2}^{\mu_{1}}}\) \(\boldsymbol{E_{1}^{\mu _{2}}}\) \(\boldsymbol{E_{2}^{\mu_{2}}}\)
5.0E − 01 2.19973047E − 01 6.25280883E − 01 2.37722314E − 01 6.75733186E − 01
1.0E − 01 4.84352308E − 02 1.37678794E − 01 5.74458438E − 02 1.63291769E − 01
5.0E − 02 2.61788488E − 02 7.44142701E − 02 2.83719452E − 02 8.06482211E − 02
1.0E − 02 8.18020277E − 03 2.32525051E − 02 8.06299020E − 03 2.29193244E − 02
5.0E − 03 5.77361943E − 03 1.64117100E − 02 5.73993055E − 03 1.63159482E − 02
1.0E − 03 4.80971954E − 03 1.36717917E − 02 4.54649392E − 03 1.29235639E − 02
5.0E − 04 4.67487514E − 03 1.32884919E − 02 4.54039711E − 03 1.29062335E − 02
1.0E − 04 4.48497982E − 03 1.27487080E − 02 4.41615901E − 03 1.25530824E − 02
5.0E − 05 4.44987772E − 03 1.26489290E − 02 4.41003343E − 03 1.25356703E − 02
1.0E − 05 4.41942400E − 03 1.25623633E − 02 4.40598999E − 03 1.25241767E − 02