Page 106 - Excel for Scientists and Engineers: Numerical Methods

CHAPTER 5 INTERPOLATION 83

Interpolation

Often it's necessary to interpolate between values in a table. You can use
simple linear interpolation, which uses a straight line relationship between two
adjacent values. Linear interpolation can be adequate if the table values are close
together, as in Figure 5-6. Most often, though, an interpolation formula that fits a
curve through several data points is necessary; cubic interpolation, in which four
data points are used for interpolation, is common. The following sections
describe methods for performing linear interpolation or cubic interpolation.

Linear Interpolation in a Table
by Means of Worksheet Formulas

To find the value of y at a point x that is intermediate between the table
values xo, yo and XI, y1, use the equation for simple linear interpolation (equation
5-1).

40

20
L
0
.- O
ti-
r
0
Q
CI)
r
'ij -20
a
f!
L
-40

-60
0 10 20 30 40 50 60
Wt% Ethylene Glycol

Figure 5-6. Freezing point of ethylene glycol solutions (data fkom Figure 5-1).
(folder 'Chapter 05 Interpolation', workbook 'Interpolation 1', sheet 'Linear Interpolation')