TI-30Xa and HP 12C: Linear Interpolation
Introduction
Given two points (x0, y0) and (x1, y1), and a point, x, we can easily estimate the y coordinate:
y = y0 + (x – x0) * (y1 – y0) / (x1 – x0)
Note that the slope of the line is:
m = (y1 – y0) / (x1 – x0)
This works the best when x is relatively real close to x0 and x1.
Fun fact, the y-intercept, where x = 0 can be calculated as:
b = y0 – x0 * m
TI-30Xa Algorithm: Linear Interpolation
This algorithm will require to enter information only once.
Store the following points:
x0 [ STO ] 1
y0 [ STO ] 2
Predict y:
[ ( ] x [ - ] [ RCL ] 1 [ ) ] [ × ] [ ( ] y1 [ - ] [ RCL ] 2 [ ) ] [ ÷ ] [ ( ] x1 [ - ] [ RCL ] 1 [ ) ] [ + ] y0 [ = ]
HP 12C Algorithm: Linear Interpolation
It turns out that we can use the linear regression functions for linear interpolation. Entering two points for linear regression will create a perfect line (with the correlation of 1 or -1). The algorithm presented is for the HP 12C, and a algorithm for other calculators can easily be made.
Keystrokes:
Enter (x0, y0) and (x1, y1):
[ f ] [ Clx ] (CLEAR FIN)
y0 [ ENTER ] x0 [ Σ+ ]
y1 [ ENTER ] x1 [ Σ+ ]
To calculate y:
x [ g ] [ 2 ] (y-hat, r)
Examples
Examples |
X0 |
Y0 |
X1 |
Y1 |
X (Input) |
Y (Output) |
1 |
10 |
4.95 |
12 |
5.06 |
11 |
5.0050 |
2 |
21 |
48,057 |
23 |
52,165 |
22 |
50,111 |
3 |
1000 |
97.7 |
2000 |
94.2 |
1500 |
95.95 |
Source
“Linear interpolation” Wikipedia. Was Edited August 27, 2024. Retrieved September 4, 2024. https://en.wikipedia.org/wiki/Linear_interpolation
Until next time, as we head into the final month of 2024,
Eddie
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