DiscreteDistribution
September 12, 2024ConvergenceBisection
September 12, 2024ConvergenceBisection
Question 1

The convergence of the bisection method is
Cubic


Quadratic


Linear


none

Question 1 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 1 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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