Bisection Method

2

x

2

-1

cos(x)

x



-2-x

10(x-1.1)(x-0.8)(x-0.6)

iteration step

1

|

This Demonstration shows the steps of the bisection root-finding method for a set of functions. You can choose the initial interval by dragging the vertical, dashed lines. Each iteration step halves the current interval into two subintervals; the next interval in the sequence is the subinterval with a sign change for the function (indicated by the red horizontal lines). The method always converges to a root of

f

if

f

is continuous and

f(a)

and

f(b)

have opposite sign.