»ã±¨±êÌâ (Title)£ºA regularizing multilevel approach for nonlinear inverse problems£¨·ÇÏßÐÔ·´ÎÊÌâµÄÒ»ÖÖÕýÔò»¯¶àµµ´Î²½Ö裩

»ã±¨ÈË (Speaker)£º ÍõÞ± ½ÌÊÚ£¨¼ÎÐË´óѧ£©

»ã±¨¹¦·ò (Time)£º2025Äê3ÔÂ13ÈÕ(ÖÜËÄ) 19:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒé(516 391 552)

Ô¼ÇëÈË(Inviter)£ºÖìÅå³É ½ÌÊÚ

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»ã±¨ÌáÒª£ºIn this talk, we propose a multilevel method for solving nonlinear ill-posed problems F(x) = y in Banach spaces. By minimizing the discretized version of the regularized functionals for different discretization levels, we define a sequence of regularized approximations to the exact solution, which is shown to be stable and globally convergent for arbitrary initial guesses. The penalty terms $\Theta$ in regularized functionals are allowed to be non-smooth to include $L^p-L^1$ or $L^p-$TV (total variation) cases, which are important in reconstructing special features of solutions such as sparsity and discontinuities. Two parameter identification examples are presented to validate the theoretical analysis and verify the method's effectiveness.