ACM Transactions on Mathematical Software (TOMS)
Scalable iterative solution of sparse linear systems
Parallel Computing
Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients
ACM Transactions on Mathematical Software (TOMS)
Algorithm 809: PREQN: Fortran 77 subroutines for preconditioning the conjugate gradient method
ACM Transactions on Mathematical Software (TOMS)
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
The Korean Journal of Computational & Applied Mathematics
Sourcebook of parallel computing
Computational Optimization and Applications
Advances in Engineering Software
Efficient solution for Galerkin-based polynomial chaos expansion systems
Advances in Engineering Software
Error estimation and mesh adaptation for Signorini-Coulomb problems using E-FEM
Computers and Structures
Fast iterative solvers for thin structures
Finite Elements in Analysis and Design
Multi-pass mapping schemes for parallel sparse matrix computations
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
An Empirical Analysis of the Performance of Preconditioners for SPD Systems
ACM Transactions on Mathematical Software (TOMS)
Deterministic random walk preconditioning for power grid analysis
Proceedings of the International Conference on Computer-Aided Design
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Incomplete factorization has been shown to be a good preconditioner for the conjugate gradient method on a wide variety of problems. It is well known that allowing some fill-in during the incomplete factorization can significantly reduce the number of iterations needed for convergence. Allowing fill-in, however, increases the time for the factorization and for the triangular system solutions. Additionally, it is difficult to predict a priori how much fill-in to allow and how to allow it. The unpredictability of the required storage/work and the unknown benefits of the additional fill-in make such strategies impractical to use in many situations. In this article we motivate, and then present, two “black-box” strategies that significantly increase the effectiveness of incomplete Cholesky factorization as a preconditioner. These strategies require no parameters from the user and do not increase the cost of the triangular system solutions. Efficient implementations for these algorithms are described. These algorithms are shown to be successful for a variety of problems from the Harwell-Boeing sparse matrix collection.