When compared to the Jacobi method, the Gauss-Siedel method ____________

has less convergence and needs more memory

has better convergence and needs less memory

has less convergence and needs more memory

has less convergence and needs less memory

has better convergence and needs more memory

Which of these statements is incorrect about iterative methods?

Not suitable for sparse matrices

Explore topic-wise MCQs in Computational Fluid Dynamics.

This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Computational Fluid Dynamics knowledge and support exam preparation. Choose a topic below to get started.

1.	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<sup>2</sup>
Answer» D. LL<sup>2</sup>

Discussion

2.	Which of these methods is not restricted to symmetric positive definite matrices?
A.	The method of steepest descent
B.	Conjugate gradient method
C.	Bi-conjugate gradient method
D.	Gauss-Seidel method
Answer» E.

Discussion

3.	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
Answer» B. ILU decomposition

Discussion

4.	What does the letter I stand for in ILU decomposition problem?
A.	Inbuilt
B.	Incomplete
C.	Iterative
D.	Imbalanced
Answer» C. Iterative

Discussion

5.	Preconditioners improve ____________ of the coefficient matrix.
A.	sparsity
B.	rank
C.	spectral properties
D.	Singularity
Answer» D. Singularity

Discussion

6.	When compared to the Jacobi method, the Gauss-Siedel method ____________
A.	has better convergence and needs less memory
B.	has less convergence and needs more memory
C.	has less convergence and needs less memory
D.	has better convergence and needs more memory
Answer» B. has less convergence and needs more memory

Discussion

7.	Consider the global matrix A =b. What is the residual at the ith iteration? (Note: _i is the value of in the i^th iteration).
A.	A <sup>i-1</sup>+b
B.	A <sup>i-1</sup>-b
C.	A <sup>i</sup>+b
D.	A <sup>i</sup>-b
Answer» E.

Discussion

8.	Consider the global matrix A =b. Let the coefficient matrix A=M-N. At the i^th iteration, the general form can be given as ______________ (Note: ⁱ is the value of in the i^th iteration).
A.	M <sup>i</sup>=N <sup>i-1</sup>+b
B.	M <sup>i</sup>=N <sup>i</sup>+b
C.	M <sup>i</sup>=N <sup>i-1</sup>-b
D.	M <sup>i</sup>=N <sup>i</sup>-b
Answer» B. M <sup>i</sup>=N <sup>i</sup>+b

Discussion

9.	Which of these statements is incorrect about iterative methods?
A.	Low computational cost
B.	Low computer storage
C.	Not suitable for sparse matrices
D.	Needs initial guess
Answer» D. Needs initial guess

Discussion

Explore topic-wise MCQs in Computational Fluid Dynamics.

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).

Which of these methods is not restricted to symmetric positive definite matrices?

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?

What does the letter I stand for in ILU decomposition problem?

Preconditioners improve ____________ of the coefficient matrix.

When compared to the Jacobi method, the Gauss-Siedel method ____________

Consider the global matrix A =b. What is the residual at the ith iteration? (Note: i is the value of in the ith iteration).

Consider the global matrix A =b. Let the coefficient matrix A=M-N. At the ith iteration, the general form can be given as ______________ (Note: i is the value of in the ith iteration).

Which of these statements is incorrect about iterative methods?

Consider the global matrix A =b. What is the residual at the ith iteration? (Note: _i is the value of in the i^th iteration).

Consider the global matrix A =b. Let the coefficient matrix A=M-N. At the i^th iteration, the general form can be given as ______________ (Note: ⁱ is the value of in the i^th iteration).