Spectral Analysis of Saddle-point Matrices from Optimization problems with Elliptic PDE Constraints

zbMath1466.62395arXiv1903.01869MaRDI QIDQ4989691

Isabella Furci, Fabio Durastante

Publication date: 26 May 2021

Full work available at URL: https://arxiv.org/abs/1903.01869

zbMATH Keywords

optimal controlpreconditioningsaddle-point matricesGLT (Generalized Locally Toeplitz) theory

Mathematics Subject Classification ID

Inference from stochastic processes and spectral analysis (62M15) Toeplitz, Cauchy, and related matrices (15B05) Preconditioners for iterative methods (65F08)

Related Items (2)

Symbol based convergence analysis in block multigrid methods with applications for Stokes problems ⋮ Optimal Block Preconditioner for an Efficient Numerical Solution of the Elliptic Optimal Control Problems Using Gmres Solver

Uses Software

• FEniCS
• FFC

Cites Work

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• Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems
• Block preconditioners for elliptic PDE-constrained optimization problems
• Automated solution of differential equations by the finite element method. The FEniCS book
• The GLT class as a generalized Fourier analysis and applications
• Exact formulae and matrix-less eigensolvers for block banded symmetric Toeplitz matrices
• Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem
• Fractional PDE constrained optimization: an optimize-then-discretize approach with L-BFGS and approximate inverse preconditioning
• Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
• Spectral analysis of inexact constraint preconditioning for symmetric saddle point matrices
• Some preconditioners for elliptic PDE-constrained optimization problems
• Block generalized locally Toeplitz sequences: from the theory to the applications
• On the eigenvalues of a class of saddle point matrices
• The Antitriangular Factorization of Saddle Point Matrices
• Generalized Locally Toeplitz Sequences: Theory and Applications
• Block-triangular preconditioners for PDE-constrained optimization
• Numerical solution of saddle point problems
• Spectral Analysis of Saddle Point Matrices with Indefinite Leading Blocks
• Eigenvalue estimates for preconditioned saddle point matrices
• A Preconditioned Iterative Method for Saddlepoint Problems
• Asymptotic Results on the Spectra of Block Toeplitz Preconditioned Matrices
• A Note on Preconditioning for Indefinite Linear Systems
• Are the Eigenvalues of Banded Symmetric Toeplitz Matrices Known in Almost Closed Form?
• Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations
• On eigenvalue distribution of constraint‐preconditioned symmetric saddle point matrices
• A note on the spectral distribution of toeplitz matrices
• Generalized Locally Toeplitz Sequences: Theory and Applications
• How to Deduce a Proper Eigenvalue Cluster from a Proper Singular Value Cluster in the Nonnormal Case
• Fractional PDE Constrained Optimization: Box and Sparse Constrained Problems
• Finite Elements

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