The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates x_a and x_b for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(x_b)is very small and then x_b 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 stepsof the secant method?
Secant Initialize: x_a, x_b, ε, N // ε = convergence indicator // N = maximum no. of iterations f_b = f(x_b) i = 0 while (i < N and |f_b| > ε) do i = i + 1 // update counter x_t = ? //missing expression for // intermediate value x_a = x_b // reset x_a x_b = x_t //reset x_b f_b = f(x_b) //function value at new xb end while if |fb| > ε then // loop is terminated with i = N write “Non - convergence” else write “return x_b” end if

Question

The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates x_a and x_b for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(x_b)is very small and then x_b 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 stepsof the secant method?

 
Secant 
Initialize: x_a, x_b, ε, N                              // ε = convergence indicator 
// N = maximum no. of iterations 
f_b = f(x_b) 
i = 0 
while (i < N and |f_b| > ε) do 
i = i + 1                                                 // update counter 
x_t = ?                                                    //missing expression for 
                                                            // intermediate value 
x_a = x_b                                                 // reset x_a 
x_b = x_t                                                 //reset x_b 
f_b = f(x_b)                                             //function value at new xb end while 
if |fb| > ε then                                     // loop is terminated with i = N 
write “Non - convergence” 
else 
write “return x_b” 
end if

Examsnet · Accepted Answer

Correct Answer is : xb – (xb – xa)fb/(fb – f(xa))

GATE Computer Science (CS) 2015 Shift 2 Solved Paper