Linear interpolation

Interpolation, in general, is a method for calculating certain intermediate values of a particular studied quantity based on a set of known values.

If the studied process can be described by a linear function, the procedure for calculating unknown parameters compared to other cases of calculation can be significantly simplified. Mathematical modeling of various production situations in engineering and scientific practice by methods of linear interpolation implies the possibility of mathematical forecasting through identifying the value of the interpolated coordinate Y by a given parameter of the coordinate X with known coordinates of two points of the linear function.

For successful management, it is necessary to predict how a particular system will behave within the existing process described by the corresponding linear function. The first point of the linear function has coordinates X0,Y0, the second - X1,Y1, the calculated resulting interpolated coordinate Y by the given coordinate value X is calculated from the formula (( X — X0 ) x ( Y1 — Y0) / ( X1 — X0) ) + Y0.

In practice, sometimes it is necessary to compare the obtained value of the parameters of the third point (X,Y) on the line with some limit value X lim,Y lim.