example of divided difference interpolaton

To illustrate how one interpolates a functionMathworldPlanetmath using divided differencesDlmfMathworldPlanetmath, we will interpolate sin40 from the sines of 0, 30, 45, 60, and 90. To keep from having too many zeros in our numbers, we will actually interpolate sin(10x) instead.

We begin by making a divided difference table:


Reading off the top numbers from each column, we may form the following divided difference series:

sin(10x)=0.1667x-0.00636x(x-3) -0.001786x(x-3)(x-4.5)

Substituting 0.4 for x, we obtain 0.6502 as an approximate value for sin40. When compared with the actual value of 0.6428, this is a reasonable approximation —it is correct to 1%.

Title example of divided difference interpolaton
Canonical name ExampleOfDividedDifferenceInterpolaton
Date of creation 2013-03-22 16:49:19
Last modified on 2013-03-22 16:49:19
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 6
Author rspuzio (6075)
Entry type Example
Classification msc 39A70