Convergence-Bisection
September 12, 2024UGC NET CS 2006 Dec-paper-2
September 12, 2024Convergence-Bisection
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Question 2
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The convergence of the bisection method is
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Cubic
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Quadratic
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Linear
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none
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Question 2 Explanation:
The convergence of the bisection method is very slow. Although the error, in general, does not decrease monotonically, the average rate of convergence is 1/2 and so, slightly changing the definition of order of convergence, it is possible to say that the method converges linearly with rate 1/2.
Note:For the bisection you simply have that ε i+1 /ε i =1/2, so, by definition the order of convergence
is 1 (linearly).
Note:For the bisection you simply have that ε i+1 /ε i =1/2, so, by definition the order of convergence
is 1 (linearly).
Correct Answer: C
Question 2 Explanation:
The convergence of the bisection method is very slow. Although the error, in general, does not decrease monotonically, the average rate of convergence is 1/2 and so, slightly changing the definition of order of convergence, it is possible to say that the method converges linearly with rate 1/2.
Note:For the bisection you simply have that ε i+1 /ε i =1/2, so, by definition the order of convergence
is 1 (linearly).
Note:For the bisection you simply have that ε i+1 /ε i =1/2, so, by definition the order of convergence
is 1 (linearly).
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