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Comparison of a-posteriori parameter choice rules for linear discrete ill-posed problems. (English) Zbl 1441.65045
The authors start from a modification of the discrepancy principle, proposed independently by H. Gfrerer [Math. Comput. 49, 507–522 (1987; Zbl 0631.65056)] and T. Raus [Uch. Zap. Tartu. Gos. Univ. 672, 16–26 (1984; Zbl 0578.65050)]. They compare the corresponding a posteriori rules for determining the Tikhonov regularization parameter \(\mu\) when applied to the solution of many linear discrete ill-posed problems with different amounts of error in the data and show that in a discrete setting, the discrepancy principle generally gives a value of \(\mu\) that yields a computed solution of higher quality than the value of \(\mu\) provided by the modified discrepancy principle.
MSC:
65F22 Ill-posedness and regularization problems in numerical linear algebra
65F10 Iterative numerical methods for linear systems
65R32 Numerical methods for inverse problems for integral equations
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