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For decreasing the number of iterations in Newton Raphson method:
- a)The value of f’(x) must be increased
- b)The value of f’’(x) must be decreased
- c)The value of f’(x) must be decreased
- d)The value of f’’(x) must be increased
Correct answer is option 'A'. Can you explain this answer?
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For decreasing the number of iterations in Newton Raphson method:a)The...
In order to decrease the number of iterations in the Newton-Raphson method, it is important to choose an initial guess that is close to the root of the function. This is because the method updates the guess by iteratively applying the formula:
x_{n+1} = x_n - (f(x_n) / f'(x_n))
where x_n is the current guess, f(x_n) is the value of the function at x_n, and f'(x_n) is the derivative of the function at x_n.
By choosing an initial guess that is close to the root, the subsequent guesses will also be closer to the root, reducing the number of iterations needed to converge to the desired accuracy.
Additionally, selecting a function that has a steeper slope near the root can also help decrease the number of iterations. This is because the Newton-Raphson method converges faster for functions with larger derivatives.
In summary, to decrease the number of iterations in the Newton-Raphson method:
- Choose an initial guess that is close to the root.
- Select a function with a steeper slope near the root.
x_{n+1} = x_n - (f(x_n) / f'(x_n))
where x_n is the current guess, f(x_n) is the value of the function at x_n, and f'(x_n) is the derivative of the function at x_n.
By choosing an initial guess that is close to the root, the subsequent guesses will also be closer to the root, reducing the number of iterations needed to converge to the desired accuracy.
Additionally, selecting a function that has a steeper slope near the root can also help decrease the number of iterations. This is because the Newton-Raphson method converges faster for functions with larger derivatives.
In summary, to decrease the number of iterations in the Newton-Raphson method:
- Choose an initial guess that is close to the root.
- Select a function with a steeper slope near the root.
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For decreasing the number of iterations in Newton Raphson method:a)The...
Iterative formula is given by
Hence if f’(x) decreases the value of next iteration approaches the initial one. This decreases the number of iterations in finding out next iterative value.
Hence if f’(x) decreases the value of next iteration approaches the initial one. This decreases the number of iterations in finding out next iterative value.
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For decreasing the number of iterations in Newton Raphson method:a)The value of f’(x) must be increasedb)The value of f’’(x) must be decreasedc)The value of f’(x) must be decreasedd)The value of f’’(x) must be increasedCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about For decreasing the number of iterations in Newton Raphson method:a)The value of f’(x) must be increasedb)The value of f’’(x) must be decreasedc)The value of f’(x) must be decreasedd)The value of f’’(x) must be increasedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For decreasing the number of iterations in Newton Raphson method:a)The value of f’(x) must be increasedb)The value of f’’(x) must be decreasedc)The value of f’(x) must be decreasedd)The value of f’’(x) must be increasedCorrect answer is option 'A'. Can you explain this answer?.
For decreasing the number of iterations in Newton Raphson method:a)The value of f’(x) must be increasedb)The value of f’’(x) must be decreasedc)The value of f’(x) must be decreasedd)The value of f’’(x) must be increasedCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about For decreasing the number of iterations in Newton Raphson method:a)The value of f’(x) must be increasedb)The value of f’’(x) must be decreasedc)The value of f’(x) must be decreasedd)The value of f’’(x) must be increasedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For decreasing the number of iterations in Newton Raphson method:a)The value of f’(x) must be increasedb)The value of f’’(x) must be decreasedc)The value of f’(x) must be decreasedd)The value of f’’(x) must be increasedCorrect answer is option 'A'. Can you explain this answer?.
Solutions for For decreasing the number of iterations in Newton Raphson method:a)The value of f’(x) must be increasedb)The value of f’’(x) must be decreasedc)The value of f’(x) must be decreasedd)The value of f’’(x) must be increasedCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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