Modified incomplete factorization strategies
Proceedings of a conference on Preconditioned conjugate gradient methods
Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
Node Selection Strategies for Bottom-Up Sparse Matrix Ordering
SIAM Journal on Matrix Analysis and Applications
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Performance of Greedy Ordering Heuristics for Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients
ACM Transactions on Mathematical Software (TOMS)
Scientific Computing
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
Effective Preconditioning through Ordering Interleaved with Incomplete Factorization
SIAM Journal on Matrix Analysis and Applications
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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In science and engineering, modeling and simulations are popularly used to gather knowledge and explain a complicated phenomena. These models are typically represented in partial differential equations (PDEs) which can be solved using meshes and sparse matrices. The solution cost of PDEs are dominated by the solution cost of sparse linear systems. Therefore, an efficient sparse linear solver becomes more important with the popularity of scientific modeling and simulations. In this paper, we proposed a robust incomplete LU preconditioning algorithm using constraints diagonal Markowitz. Experimental results with various linear systems show that ILU algorithm using constraints diagonal Markowitz shows better performance and more stable than traditional ILU algorithm with predefined ordering.