D. Haugli, Lecturer Aer E 161 Aerospace Engineering
2/11/2005 The Interpolation Method, Page 1 Iowa State University
The Interpolation Method
Whereas the bisection method uses simple averaging between left and right bounds to estimate a
root, the interpolation (or “false-position method”) uses linear interpolation to obtain improved
estimates. Both methods are examples of bracketing methods.
Graphically, the interpolation method can be visualized by drawing a line between the left and
right guesses. As shown in Figure 1, the root, 0
x, is approximated where the line intersects the
x-axis. Note that the average of l
x and r
x would yield a value of 0
x much further from the root.
The interpolation method has the advantage of honing in on the root very quickly, and generally
requires fewer iterations than the bisection method.
Figure 1. A graphical depiction of the interpolation method.
The equation for 0
x can be derived as follows. Recall the linear interpolation formula,
()
1
12
12
1xx
xx
yy
yy −
−
−
=− (1)
Let l
xx =
1, and r
xx =
2. Noting that
()
xfy =, rewrite the formula as,
() ( ) () ()
()
l
lr
lr
lxx
xx
xfxf
xfxf −
−
−
=− (2)
