arrays - Predict a value outside a 2d matrix - (2d regression?)

Question

Not quite sure what the name for this problem is which makes it hard to find a solution.

I have 2 values like [ 0, 2.5 ] each describing an index for 2 dimensional array. X/Y-Axis has a scale of [0, 0.2, 0.3, 0.4 ... 2.5] - so for the example i get indexX: 0 indexY: N.

Now i can pic the resulting value at position [0, N] from the 2D-Array. My Problem is - i can now get values outside of the 2D-Array, like [ 2.6, 2.6 ]. How can i predict a value for this coordinates.

Any hints on this - i used simple linear regressions for predicting simple pair of values but don't know what the name for this mathematical problem is and how to solve it?

question from:https://stackoverflow.com/questions/65848869/predict-a-value-outside-a-2d-matrix-2d-regression

Answer 1

You could use some form of interpolating polynomial, e.g. Lagrange interpolation or Newtonian interpolation. You have a function described by the values in your array [0, 0.2, 0.3, ..., 2.5]. You can then use one of the interpolation methods to basically map the indexes of your array [0, 1, 2, ..., N] to the values. See Lagrange polynomial and Newton polynomial for details. Be aware that using these to interpolate values outside the defined range of the function can be problematic, and that linear interpolation may provide better results if your values are, in fact, linear.