,MULTI-PARAMETER TIKHONOV REGULARIZATION FOR LINEAR ILL-POSED OPERATOR EQUATIONS

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We consider solving linear ill-posed operator equations.Based on a multi-scale decomposition for the solution space,we propose a multi-parameter regularization for solving the equations.We establish weak and strong convergence theorems for the multi-parameter regularization solution.In particular,based on the eigenfunction decomposition,we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound.Several practical choices of multi-parameters are proposed.We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.Mathematics subject classification:47A52.
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