Linear interpolation is a procedure widely used to estimate the values that a function takes in a range of which we know its values at the extremes (x1, f (x1)) and (x2, f (x2)).
To estimate this value we use the approximation to the function f (x) by means of a line r (x) (hence the name of linear interpolation, since quadratic interpolation also exists). The expression of the linear interpolation is obtained from the one-degree Newton interpolator polynomial.
LINEAR INTERPOLATION STRAIGHT
Let's see the steps that we have to follow to find the regression line:
1. Given the points of the function (x1, y1) and (x2, y2), we want to estimate the value of the function at a point x in the interval x1 <x <x2.
2. To find the line of interpolation we will look at the following image.
For this we use the similarity of the ABD and CAE triangles, obtaining the following proportionality of segments: AB / AC = BD / CE.
3. Clearing the segment BD (since the point D is the one that we do not know) we obtain: BD = (AB / AC) ∙ CE. Translating to algebraic language we obtain that:
And clearing, we get:
The same expression that is obtained when using the interpolator polynomial of Newton that we had already commented. Remember that y1 = f (x1) and likewise y2 = f (x2).
Look an example of where you can apply this procedure
