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
Matrix computations (3rd ed.)
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
Incomplete Cholesky Factorizations with Limited Memory
SIAM Journal on Scientific Computing
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
On the Incomplete Cholesky Decomposition of a Class of Perturbed Matrices
SIAM Journal on Scientific Computing
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Robust Preconditioner with Low Memory Requirements for Large Sparse Least Squares Problems
SIAM Journal on Scientific Computing
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Modified Gauss-Newton scheme with worst case guarantees for global performance
Optimization Methods & Software
A Subspace Minimization Method for the Trust-Region Step
SIAM Journal on Optimization
Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares
SIAM Journal on Numerical Analysis
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.00 |
We present a technique for building effective and low cost preconditioners for sequences of shifted linear systems $(A + \alpha I) x_\alpha = b$, where $A$ is symmetric positive definite and $\alpha 0$. This technique updates a preconditioner for $A$, available in the form of an $LDL^T$ factorization, by modifying only the nonzero entries of the $L$ factor in such a way that the resulting preconditioner mimics the diagonal of the shifted matrix and reproduces its overall behavior. This approach is supported by a theoretical analysis as well as by numerical experiments, showing that it works efficiently for a broad range of values of $\alpha$.