Question:
The order of the convergence of the bisection method is
The order of the convergence of the bisection method is
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Bisection method converges slowly but reliably—it has **linear convergence**, hence order 1.
Updated On: May 21, 2025
- \( 4 \)
- \( 2 \)
- \( 1 \)
- \( 3 \)
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The Correct Option is C
Solution and Explanation
The bisection method is a bracketing method where the interval size reduces by half each iteration. The error after \( n \) steps is bounded by:
\[
|x_n - x^*| \leq \frac{b - a}{2^n}
\]
This implies linear convergence, which is convergence of order \( 1 \).
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