A local convergence theory for combined inexact-Newton/finite-difference projection methods
SIAM Journal on Numerical Analysis
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
A new sparsity preserving quasi-Newton update for solving nonlinear equations
SIAM Journal on Scientific and Statistical Computing
Inexact trust region method for large sparse systems of nonlinear equations
Journal of Optimization Theory and Applications
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Decay Rates of the Inverse of Nonsymmetric Tridiagonal and Band Matrices
SIAM Journal on Matrix Analysis and Applications
A comparative study of sparse approximate inverse preconditioners
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Scalable Parallel Preconditioning with the Sparse Approximate Inverse of Triangular Matrices
SIAM Journal on Matrix Analysis and Applications
On the Incomplete Cholesky Decomposition of a Class of Perturbed Matrices
SIAM Journal on Scientific Computing
A Globally Convergent Newton-GMRES Subspace Method for Systems of Nonlinear Equations
SIAM Journal on Scientific Computing
Automatic Preconditioning by Limited Memory Quasi-Newton Updating
SIAM Journal on Optimization
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Subspace Trust-Region Methods for Large Bound-Constrained Nonlinear Equations
SIAM Journal on Numerical Analysis
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
Journal of Computational Physics
Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
On Using Approximate Finite Differences in Matrix-Free Newton-Krylov Methods
SIAM Journal on Numerical Analysis
Preconditioner updates applied to CFD model problems
Applied Numerical Mathematics
Updating preconditioners for nonlinear deblurring and denoising image restoration
Applied Numerical Mathematics
Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares
SIAM Journal on Numerical Analysis
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Newton-Krylov methods, a combination of Newton-like methods and Krylov subspace methods for solving the Newton equations, often need adequate preconditioning in order to be successful. Approximations of the Jacobian matrices are required to form preconditioners, and this step is very often the dominant cost of Newton-Krylov methods. Therefore, working with preconditioners may destroy the “Jacobian-free” (or matrix-free) setting where the single Jacobian-vector product can be provided without forming and storing the element of the true Jacobian. In this paper, we propose and analyze a preconditioning technique for sequences of nonsymmetric Jacobian matrices based on the update of an earlier preconditioner. The proposed strategy can be implemented in a matrix-free manner. Numerical experiments on popular test problems confirm the effectiveness of the approach in comparison with the standard ILU-preconditioned Newton-Krylov approaches.