Spectral Analysis of Block Diagonally Preconditioned Multiple Saddle-Point Matrices with Inexact Schur Complements

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 [Bergamaschi et al., Linear Algebra and its Applications, 2026]. Numerical experiments are carried out to validate the proposed estimates.

Source: arXiv:2602.05952v1 - http://arxiv.org/abs/2602.05952v1 PDF: https://arxiv.org/pdf/2602.05952v1 Original Article: View on arXiv