Minimization of the Tikhonov functional in Banach spaces smooth and convex of power type by steepest descent in the dual

For Tikhonov functionals of the form Ψ(x)=‖Ax−y‖Yr+α‖x‖Xq we investigate a steepest descent method in the dual of the Banach space X. We show convergence rates for the proposed method and present numerical tests.

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