JuliaSmoothOptimizers / LimitedLDLFactorizations.jl

Limited-Memory Factorization of Symmetric Matrices
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Support for Modified Incomplete Choleksy Decomposition #42

Open RoyiAvital opened 3 years ago

RoyiAvital commented 3 years ago

In the book Yousef Saad - Iterative Methods for Sparse Linear Systems (2nd Edition):

image

This method, originally for the ILU decomposition, can improve the performance of the conditioner greatly. Basically it enforces the conditioner to comply A e = L L' e where e is a vector of ones. Namely the sum of values of a row matches the input matrix.
The way it is implemented is that any component which is dropped in the incomplete decomposition is compensated by the diagonal component.

Since component of the row is computed anyway it should come almost freely (Unless I'm wrong and the values are not computed).