Spectral Analysis of Block Diagonally Preconditioned Multiple Saddle‐Point Matrices With Inexact Schur Complements

ABSTRACT We derive eigenvalue bounds for symmetric block‐tridiagonal multiple saddle‐point systems preconditioned with block‐diagonal Schur complement matrices. This analysis applies to an arbitrary number of blocks and accounts for the case where the Schur complements are approximated, generalizing the findings in [11, Bergamaschi et al., Linear Algebra and its Applications, 2026]. Numerical experiments are carried out to validate the proposed estimates.