Question

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

Answer 1

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.