# Eigenvalue Bounds for Double Saddle-Point Systems

@article{Bradley2021EigenvalueBF, title={Eigenvalue Bounds for Double Saddle-Point Systems}, author={Susanne Bradley and Chen Greif}, journal={ArXiv}, year={2021}, volume={abs/2110.13328} }

We derive bounds on the eigenvalues of a generic form of double saddle-point matrices. The bounds are expressed in terms of extremal eigenvalues and singular values of the associated block matrices. Inertia and algebraic multiplicity of eigenvalues are considered as well. The analysis includes bounds for preconditioned matrices based on block diagonal preconditioners using Schur complements, and it is shown that in this case the eigenvalues are clustered within a few intervals bounded away from…

## One Citation

A Preconditioned Inexact Active-Set Method for Large-Scale Nonlinear Optimal Control Problems

- Computer Science, MathematicsArXiv
- 2021

A global convergence proof of the recently proposed sequential homotopy method with an inexact Krylov–semismooth-Newton method employed as a local solver and an efficient, parallelizable, symmetric positive definite preconditioner based on a double Schur complement approach is provided.

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