GATE CS 2015 Set 2 — Question 51
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Engineering Mathematics → Calculus
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Question
The secant method is used to find the root of an equation . It is started from two distinct estimates and for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if is very small and then is the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by ?. Which is the suitable expression that is to be put in place of ? so that it follows all steps of the secant method?
Secant
Initialize: xa, xb, epsilon, N // epsilon = convergence indicator
// N = maximum no. of iterations
fb = f(xb)
i = 0
while (i < N and |fb| > epsilon) do
i = i + 1 // update counter
xt = ? // missing expression for
// intermediate value
xa = xb // reset xa
xb = xt // reset xb
fb = f(xb) // function value at new xb
end while
if |fb| > epsilon then // loop is terminated with i=N
write "Non-convergence"
else
write "return xb"
end if
Correct answer
(C) x_b - (x_b - xₐ) f_b / (f_b - f(xₐ))
Solution
The Secant method formula for the next approximation given and is:In the given code:
- corresponds to the current approximation .
- corresponds to the previous approximation .
- holds .
- is the new approximation .
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