Interpolation

Description

This article describes linear and cubic spline data interpolation methods.

Model theory

This section is currently under construction. Please check back later for updates and revisions.

Excel

The interpolation methods may be invoked from the Excel formula bar with the following function calls:

=mdInterp_Linear(known_xs as Range, known_ys as Range, xs as Range)

and

=mdInterp_CubicSpline(known_xs as Range, known_ys as Range, xs as Range)

Invoking the function with no arguments will print Help text associated with the model, including a link to this page.

The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:

${\begin{aligned}{\mathit {known\_xs}}={\begin{bmatrix}x_{1}\\\vdots \\x_{n}\\\end{bmatrix}},\;\;\;\;{\mathit {known\_ys}}={\begin{bmatrix}y_{1}\\\vdots \\y_{n}\\\end{bmatrix}},\;\;\;\;{\mathit {xs}}={\begin{bmatrix}x_{1}\\\vdots \\x_{m}\\\end{bmatrix}}\;\;\;\;\end{aligned}}$ ${\begin{aligned}{\mathit {mdInterp\_Linear}}&={\begin{bmatrix}y_{1}\\\vdots \\y_{m}\\\end{bmatrix}}\\\\{\mathit {mdInterp\_CubicSpline}}&={\begin{bmatrix}y_{1}\\\vdots \\y_{m}\\\end{bmatrix}}\end{aligned}}$ where: $n$ is the number of data points $m$ is the number of interpolation points $x_{1}\cdots x_{n}$ is an array of the known independent data values $y_{1}\cdots y_{n}$ is an array of the known dependent data values $x_{1}\cdots x_{m}$ is an array of the independent data values at which the dependant variable is to be interpolated $y_{1}\cdots y_{m}$ is an array of the interpolated dependant variable values

Figure 1. Example showing the selection of the known_xs (blue frame), known_ys (red frame), xs (purple frame), and Results (light blue frame) arrays in Excel.