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.