2019/12/20 by Alexander Beigl, Beigl, Alexander, Jarle Sogn +3 · 1 citation
Computer Science · Engineering · Mathematics · #49J20 #49K20 #65F08 #65N22 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1912.09995
openalex publication_date 2019/12/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper we consider multiple saddle point problems with block\ntridiagonal Hessian in a Hilbert space setting. Well-posedness and the related\nissue of preconditioning are discussed. We give a characterization of all block\nstructured norms which ensure well-posedness of multiple saddle point problems\nas a helpful tool for constructing block diagonal preconditioners. We\nsubsequently apply our findings to a general class of PDE-constrained optimal\ncontrol problems containing a regularization parameter \α and derive\n\α-robust preconditioners for the corresponding optimality systems.\nFinally, we demonstrate the generality of our approach with two optimal control\nproblems related to the heat and the wave equation, respectively. Preliminary\nnumerical experiments support the feasibility of our method.\n