Eddie’s Math and Calculator Blog: TI-30Xa and HP 12C: Linear Interpolation

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

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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