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. Author manuscript; available in PMC: 2018 Nov 21.
Published in final edited form as: SIAM J Sci Comput. 2017 Nov 21;39(6):B1064–B1101. doi: 10.1137/16M1070475

Fig. 5.

Fig. 5

Convergence results for different strategies to precondition the reduced space KKT system. We report exemplary trends of the relative residual ‖rk‖rel := ‖rk‖2/‖r0‖2 with respect to the iteration number k. We report results for different images (top row: BRAIN; bottom row: HAND; grid size (256, 256)⊤) with respect to varying regularization weights βv (left column: βv = 1E−1; middle column: βv = 1E−2; right column: βv = 1E−3). We solve the system at the true solution available for the considered synthetic test problems. We use an H2-regularization model (compressible diffeomorphism). We use a PCG method with a tolerance of 1E−6 to solve this system. We report results for the regularization preconditioner PREG (red curve) and the nested preconditioner P2L. We use two solvers to invert the preconditioner: PCG(1E−1) (blue curve) and CHEB(10) (green curve). The results correspond to those reported in Tab. 8.