Summary: ERROR IN LINEAR INTERPOLATION
Let P1(x) denote the linear polynomial interpolating
f(x) at x0 and x1, with f(x) a given function (e.g.
f(x) = cos x). What is the error f(x) - P1(x)?
Let f(x) be twice continuously differentiable on an in-
terval [a, b] which contains the points {x0, x1}. Then
for a x b,
f(x) - P1(x) =
(x - x0) (x - x1)
2
f00(cx)
for some cx between the minimum and maximum of
x0, x1, and x.
If x1 and x are `close to x0', then
f(x) - P1(x)
(x - x0) (x - x1)
2
f00(x0)
Thus the error acts like a quadratic polynomial, with
zeros at x0 and x1.

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

Collections: Computer Technologies and Information Sciences