In incomplete Cholesky decomposition, the preconditioner matrix

in-incomplete-cholesky-decomposition-the-preconditioner-matrix

In incomplete Cholesky decomposition, the preconditioner matrix produced is ____________ (Note: L is the factorized lower triangular matrix and U is the factorized lower triangular matrix).

A. UL’

B. LU’

C. LL’

D. LL^2

I got this question at a job interview.

This intriguing question originated from Numerical Methods in section Numerical Methods of Computational Fluid Dynamics

Right choice is C. LL’

The explanation is: In incomplete Cholesky decomposition, factorization is done only for the lower triangular matrix and the preconditioner matrix is LL’. The coefficient matrix is also approximately equal to the preconditioner matrix.