The secant method is used to find the root of an equation f(x) = 0. It is…

The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xa and xb for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xb 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, ε, N // ε = convergence indicator

fb = f(xb) i = 0

while (i < N and |fb| > ε) 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| > ε

then // loop is terminated with i = N

write “Non-convergence”

else

write “return xb”

end if