Sparse Incomplete Cholesky Decomposition
Implementation of the Incomplete Cholesky Decomposition with few methods.
The project includes a
C implementation with a MATLAB MEX wrapper.
The aim is to have 3 variants of the incomplete decomposition:
- Threshold (
Using a threshold, $ \tau $ to define which elements will be kept from the decomposition.
It can be using global threshold or by a column.
- Pattern (
Filling elements which are up to
lsteps in the graph of the matrix
l = 0called Zero Fill where filling zeros in elements not defined by the pattern.
Also could be filled by a given pattern of sparsity (So given
Aas the pattern it matches
l = 0).
- Number of Non Zero Elements (
Keeps the largest
pelements per column.
Generating MATLAB MEX
- Download the repository.
MakeMexin MATLAB with pre defined MATLAB MEX Compiler.
- Go through the Unit Tests and the Run Time Analysis.
The MEX Wrapper supports only Sparse Real Matrices of Type Double.
Comparing the performance with MATLAB's functions.
The MEX file and MATLAB's
ICT were the most memory efficient.
Pre Conditioning (Solving the Linear System)
- Move the array sorting related code to a dedicated repository with complete run time analysis.
Ccode is basically a redo of the Pre Conditioner in the Python package.
- Support Preconditioning Materials and Publications.
- An Incomplete Cholesky Factorization for Dense Symmetric Positive Definite Matrices.
- A Survey of Incomplete Factorization Preconditioners.
- Experimental Study of ILU Preconditioners for Indefinite Matrices.
- A Robust Limited Memory Incomplete Cholesky Factorization.
- Incomplete Cholesky Factorizations with Limited Memory.
- Modified Incomplete Cholesky Factorization for Solving Electromagnetic Scattering Problems.
Royi Avital (2023). Incomplete Cholesky Decomposition (https://github.com/RoyiAvital/IncompleteCholeskyDecomposition), GitHub. Retrieved .
MATLAB Release Compatibility
Platform CompatibilityWindows macOS Linux
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