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Compared to Gauss-seidel method, Newton- Raphson method takes
- a)Less number of iterations and more time per iteration
- b)Less numbers of iterations and less time per iteration
- c)More number of iterations and more time per iteration
- d)More number of iterations and less time per iteration
Correct answer is option 'A'. Can you explain this answer?
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Compared to Gauss-seidel method, Newton- Raphson method takesa)Less nu...
Newton-Raphson method and Gauss-Seidel method are two commonly used iterative methods for solving nonlinear equations. In this question, we are asked to compare these two methods in terms of the number of iterations and time per iteration.
Newton-Raphson Method:
• The Newton-Raphson method is an iterative method used to find the roots of nonlinear equations.
• It requires the first derivative of the function to be calculated.
• In each iteration, it updates the guess value using the formula Xn+1=Xn-f(Xn)/f'(Xn)
• It converges faster than other iterative methods.
Gauss-Seidel Method:
• The Gauss-Seidel method is an iterative method used to solve a system of linear equations.
• It updates the guess value for each variable in each iteration.
• It converges slower than Newton-Raphson method.
Comparison:
• The Newton-Raphson method requires the calculation of the first derivative, which is an additional calculation compared to the Gauss-Seidel method.
• However, the Newton-Raphson method converges faster than the Gauss-Seidel method. So, it requires less number of iterations to converge.
• On the other hand, the Gauss-Seidel method requires fewer calculations per iteration compared to the Newton-Raphson method. Hence, it takes less time per iteration.
• Therefore, the correct answer is option 'A', i.e., Newton-Raphson method takes less number of iterations and more time per iteration compared to the Gauss-Seidel method.
Newton-Raphson Method:
• The Newton-Raphson method is an iterative method used to find the roots of nonlinear equations.
• It requires the first derivative of the function to be calculated.
• In each iteration, it updates the guess value using the formula Xn+1=Xn-f(Xn)/f'(Xn)
• It converges faster than other iterative methods.
Gauss-Seidel Method:
• The Gauss-Seidel method is an iterative method used to solve a system of linear equations.
• It updates the guess value for each variable in each iteration.
• It converges slower than Newton-Raphson method.
Comparison:
• The Newton-Raphson method requires the calculation of the first derivative, which is an additional calculation compared to the Gauss-Seidel method.
• However, the Newton-Raphson method converges faster than the Gauss-Seidel method. So, it requires less number of iterations to converge.
• On the other hand, the Gauss-Seidel method requires fewer calculations per iteration compared to the Newton-Raphson method. Hence, it takes less time per iteration.
• Therefore, the correct answer is option 'A', i.e., Newton-Raphson method takes less number of iterations and more time per iteration compared to the Gauss-Seidel method.
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Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer?
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Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer?.
Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer?.
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Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Compared to Gauss-seidel method, Newton- Raphson method takesa)Less number of iterations and more time per iterationb)Less numbers of iterations and less time per iterationc)More number of iterations and more time per iterationd)More number of iterations and less time per iterationCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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