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In which of these methods, after factorization, the pattern of zero elements in the combined L and U matrices the same as the original coefficient matrix?

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In which of these methods, after factorization, the pattern of zero elements in the combined L and U matrices the same as the original coefficient matrix?

(a) LU decomposition

(b) ILU decomposition

(c) ILU(0) decomposition

(d) ILU(1) decomposition

I had been asked this question in an online quiz.

This is a very interesting question from Numerical Methods in section Numerical Methods of Computational Fluid Dynamics

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The correct choice is (a) LU decomposition

Best explanation: The extra non-zero elements in the factorized matrices are called fill-ins. In ILU(p), p indicates the order of fill-in allowed. So, where there is no fill-in, the pattern of combined L and U matrices and the coefficient matrix will be the same.

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