This set of Finite Element Method online test focuses on “Conjugate Gradient Method for Equation Solving”.

1. Conjugate gradient method is a ________

a) Standard method

b) Equation method

c) Iterative method

d) Elimination method

View Answer

Explanation: The conjugate gradient method is an iterative method for the solution of equations. And it is implemented in several computer codes. This method is used to solve un-constrained optimization problems such as energy minimization.

2. Conjugate gradient method is for only _________

a) Non symmetric matrix

b) Symmetric matrix

c) Symmetric and Non symmetric matrix

d) Identity matrix

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Explanation: Conjugate gradient method generally used to solve symmetric matrices. This method is often implemented as an iterative algorithm. Large sparse systems often arise when numerically solving partial differential equations or optimization problems.

3. Which version is used to solve conjugate gradient method of the algorithm of symmetric matrices?

a) Rayleighs version

b) Fletcher-Reeves version

c) Frontal method

d) Galerkins method

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Explanation: We generally present Fletcher-Reeves version of the algorithm of the symmetric matrices in Conjugate gradient method. This method is of algorithm model and also as an iterative method. Conjugate gradient method is unstable with respect to even small perturbations.

4. The iterations are continued until g_{k}^{T}g_{x} reaches a ________ (here k=0 1 2 3……)

a) Small value

b) Infinite value

c) Large value

d) Negative value

View Answer

Explanation: When k=0 1 2 3…… The iterations are continued until g

_{k}

^{T}g

_{x}reaches small value in conjugate gradient method. By getting small values we can easily conclude the problems. And also can be easily iterated to next easiest method like Gaussian elimination.

5. This method is robust and has ________ n iterations.

a) Diverges

b) Converges

c) Converge and diverge

d) Symmetric

View Answer

Explanation: When we solve a symmetric matrix in conjugate gradient method, it can be simplified in n iterations and also this method is robust and converges “n” no of iterations. Conjugate gradient method can be implemented to optimization of solution.

6. Conjugate gradient method is implemented in _________

a) Algorithm solving

b) Iterative solving

c) Program solving

d) Program CG solving

View Answer

Explanation: Conjugate gradient algorithm procedure is implemented in program CG solving, which is included on disk. This method is also easily to solve in MAT Lab also. Several algorithms have been proposed e.g., CGLS, LSQR.

7. Conjugate gradient method includes several ______

a) Computer codes

b) Programs

c) Algorithms

d) Matrices

View Answer

Explanation: Conjugate gradient method is an iterative method for the solution of equations. This method is become increasingly popular and is implemented in several computer codes. Because, it is mainly done on computer software such as MAT lab.

8. Conjugate gradient algorithm can be accelerated by using _________

a) Algorithm strategies

b) Preconditioning strategies

c) Conditioning strategies

d) Computer strategies

View Answer

Explanation: Conjugate gradient algorithm can be accelerated by using preconditioning strategies. Preconditioner of a matrix has to be symmetric positive definite and fixed and that cannot be changed from iteration to iteration. The behavior of the preconditioned conjugate gradient method may become unpredictable.

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