Eigenvalue Bounds for Symmetric, Multiple Saddle-Point Matrices with SPD Preconditioners

We derive eigenvalue bounds for symmetric block-tridiagonal multiple saddle-point systems preconditioned with the symmetric positive definite (SPD) preconditioner proposed by J. Pearson and A. Potschka in 2024, and further studied by L. Bergamaschi and coauthors, for double saddle point problems, with inexact Schur complement matrices. The analysis applies to an arbitrary number of blocks. Numerical experiments are carried out to validate the proposed estimates.