Question

Consider the global matrix AΦ=b. If my coefficient matrix A is the same for different b vectors, which of these methods is economic?

(a) Gauss elimination

(b) TDMA

(c) LU decomposition

(d) PDMA

I have been asked this question during an online exam.

My question is based upon Numerical Methods in section Numerical Methods of Computational Fluid Dynamics

Answer 1

Correct option is (c) LU decomposition

The explanation is: Once matrix A is factorized in the LU decomposition method, the same factorized matrices can be used to solve different b vectors. Because decomposition does not depend upon the b vector. This is the major advantage of the LU decomposition method.