Finite Element Method Questions and Answers – Conjugate Gradient Method for Equation Solving

«
»

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

Answer: c
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.
advertisement

2. Conjugate gradient method is for only _________
a) Non symmetric matrix
b) Symmetric matrix
c) Symmetric and Non symmetric matrix
d) Identity matrix
View Answer

Answer: b
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
View Answer

Answer: b
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.
advertisement
advertisement

4. The iterations are continued until gkTgx reaches a ________ (here k=0 1 2 3……)
a) Small value
b) Infinite value
c) Large value
d) Negative value
View Answer

Answer: a
Explanation: When k=0 1 2 3…… The iterations are continued until gkTgx 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

Answer: b
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.
advertisement

6. Conjugate gradient method is implemented in _________
a) Algorithm solving
b) Iterative solving
c) Program solving
d) Program CG solving
View Answer

Answer: d
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

Answer: a
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.
advertisement

8. Conjugate gradient algorithm can be accelerated by using _________
a) Algorithm strategies
b) Preconditioning strategies
c) Conditioning strategies
d) Computer strategies
View Answer

Answer: b
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.

Sanfoundry Global Education & Learning Series – Finite Element Method.

advertisement

To practice all areas of Finite Element Method for online tests, here is complete set of 1000+ Multiple Choice Questions and Answers.

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

advertisement
advertisement
Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter