Stein-based preconditioners for weak-constraint 4D-var

DOI10.1016/j.jcp.2023.112068OpenAlexW4324370064MaRDI QIDQ2699364

Davide Palitta, Jemima M. Tabeart

Publication date: 26 April 2023

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.17184

zbMATH Keywords

preconditioningdata assimilationStein equations4D-var

Mathematics Subject Classification ID

Numerical linear algebra (65Fxx) Basic linear algebra (15Axx) Numerical methods for mathematical programming, optimization and variational techniques (65Kxx)

Uses Software

• Manopt
• Matrix Means Toolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The ubiquitous Kronecker product
• A low-rank approach to the solution of weak constraint variational data assimilation problems
• Computing the Karcher mean of symmetric positive definite matrices
• Matrix equation techniques for certain evolutionary partial differential equations
• Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation
• On the convergence of Krylov methods with low-rank truncations
• Flexible Conjugate Gradients
• Inverse Modeling
• A Computational Method for Symmetric Stein Matrix Equations
• Manopt, a Matlab toolbox for optimization on manifolds
• A preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations
• Computational Methods for Linear Matrix Equations
• Numerical solution of saddle point problems
• A Low-Rank in Time Approach to PDE-Constrained Optimization
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Solution of Sparse Indefinite Systems of Linear Equations
• A numerical algorithm to solve<tex>A^{T}XA - X = Q</tex>
• Flexible Inner-Outer Krylov Subspace Methods
• A Note on Preconditioning for Indefinite Linear Systems
• The Riemannian Barzilai–Borwein method with nonmonotone line search and the matrix geometric mean computation
• The conditioning of least‐squares problems in variational data assimilation
• Low rank updates in preconditioning the saddle point systems arising from data assimilation problems
• The Sherman–Morrison–Woodbury formula for generalized linear matrix equations and applications
• New bounds on the condition number of the Hessian of the preconditioned variational data assimilation problem
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Methods of conjugate gradients for solving linear systems