Computational Mathematics and Scientific Computing Seminar

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Double saddle-point systems are drawing increasing attention in the past few years, due to the importance of relevant applications and the challenge in developing efficient iterative numerical solvers for these problems. In this talk we describe some numerical properties of the matrices arising from these problems. We derive eigenvalue bounds and analyze the spectrum of preconditioned matrices. We show that if Schur complements are effectively approximated, the eigenvalue structure gives rise to rapid convergence of Krylov subspace solvers. A few numerical experiments illustrate our findings.