Question Bank • QB_EM_ADV_078 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Solutions of linear and non-linear algebraic equations

Question Statement:

The asymptotic order of convergence of the secant method for finding a simple root of a non-linear algebraic equation is approximately:

Options:

  • (A) $1.618$
  • (B) $2.000$
  • (C) $1.000$
  • (D) $3.000$

Answer Key:

A

Step-by-Step Solution & Explanation

The error relationship in the secant method is $|e_{n+1}| \approx C |e_n|^p$, where $p$ is the positive root of $p^2 - p - 1 = 0$: $p = \frac{1 + \sqrt{5}}{2} \approx 1.618$ This is the golden ratio, making the secant method superlinear (faster than linear bisection, but slightly below quadratic Newton–Raphson).
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