GATE 2015 CS (CS2) – Question 51
The secant method starts with distinct estimates $x_a,x_b$ and repeatedly sets $x_t=?$, then $x_a=x_b$, $x_b=x_t$, and $f_b=f(x_b)$, stopping at small residual or the iteration limit. Which missing expression gives the secant update?
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Correct answer: (C) $x_b-(x_b-x_a)f_b/(f_b-f(x_a))$
Explanation
The secant through (xₐ,f(xₐ)) and (x_b,f_b) has slope $(f_b-f(x_a))/(x_b-x_a)$. Its x-intercept is the current x_b minus f_b divided by that slope. This yields C. It replaces the derivative in Newton’s method by a two-point finite difference.