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arXiv · 2509.11434

Variational estimates for Schur complements of symmetric saddle point problems

Jongho Park
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Abstract

We present sharp variational estimates for the extremal eigenvalues of Schur complements arising in symmetric saddle point problems. These estimates make explicit the role of right inverses with controlled energy in lower bounds and of null space corrections in upper bounds. The same argument applies to projected Schur complements when the primal operator is semidefinite. Applications to the augmented Lagrangian method, mixed finite element methods, and nonoverlapping domain decomposition methods yield concise proofs of established convergence estimates.

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Jongho Park. 2026-09-20. Variational estimates for Schur complements of symmetric saddle point problems. https://arxiv.org/abs/2509.11434

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