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Which of the following method is sensitive to starting value, when solving an algebraic equation?
- a)Method of False position
- b)Bi-section method
- c)Newton-Raphson method
- d)Trapezoidal rule
Correct answer is option 'C'. Can you explain this answer?
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Which of the following method is sensitive to starting value, when so...
Newton-Raphson method:
The Newton-Raphson method is a popular iterative method for finding the roots of a real-valued function. It is particularly efficient when the function is differentiable and smooth. However, this method is sensitive to the starting value chosen.
Explanation:
- The Newton-Raphson method requires an initial guess to start the iteration process. The method involves taking the derivative of the function at each iteration, which means that the starting point can significantly impact the convergence of the method.
- If the starting value is close to the actual root, the method will converge quickly. However, if the initial guess is far from the true root, the method may fail to converge or converge to a different root altogether.
- Choosing an appropriate starting value is crucial for the success of the Newton-Raphson method. It may require some trial and error to find a suitable initial guess that leads to convergence.
Conclusion:
In summary, the Newton-Raphson method is sensitive to the starting value because the convergence of the method depends on the initial guess chosen. It is important to carefully select the starting point to ensure the method converges to the correct root of the algebraic equation.
The Newton-Raphson method is a popular iterative method for finding the roots of a real-valued function. It is particularly efficient when the function is differentiable and smooth. However, this method is sensitive to the starting value chosen.
Explanation:
- The Newton-Raphson method requires an initial guess to start the iteration process. The method involves taking the derivative of the function at each iteration, which means that the starting point can significantly impact the convergence of the method.
- If the starting value is close to the actual root, the method will converge quickly. However, if the initial guess is far from the true root, the method may fail to converge or converge to a different root altogether.
- Choosing an appropriate starting value is crucial for the success of the Newton-Raphson method. It may require some trial and error to find a suitable initial guess that leads to convergence.
Conclusion:
In summary, the Newton-Raphson method is sensitive to the starting value because the convergence of the method depends on the initial guess chosen. It is important to carefully select the starting point to ensure the method converges to the correct root of the algebraic equation.
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Which of the following method is sensitive to starting value, when so...
Newton-Raphson method is sensitive to the starting value. If the initial guess is not sufficiently close to the root, then the method may not converge to the root.
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Which of the following method is sensitive to starting value, when solving an algebraic equation?a)Method of False positionb)Bi-section methodc)Newton-Raphson methodd)Trapezoidal ruleCorrect answer is option 'C'. Can you explain this answer?
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