## Interpolation and extrapolation in Mathcad

Under the term of Interpolation in Mathcad we understand recovery of function based on known values or values of its derivatives in isolated points. Problem of interpolation of experimental data is reduced to foreseeing in passing points value of function, defined as tabulated. Which means that initial data can be introduced in the form of a table, which incorporates discrete experimental values, obtained in some points of experimental observation or during the definite time laps. Mathcad makes it possible to join tabular points with one line (linear interpolation) or with segments of cubical polynomial (cubical spline interpolation)

Linear interpolation in Mathcad is materialized with the help of the function: linterp(vx,vy,x), where vx, vy are data vectors. Data should be arranged in ascending order; x is the argument in which value of y is returned.

Cubical spline interpolation allows to join a set of points with a smooth curve in such a way that lets the first and the second derivatives in these points be continuous. Interpolation is realized with two functions. Firstly, vector of second derivatives is calculated in points under analysis, then the value of function is figured out in the point of x -> interp(vs,vx,vy,x). A set of three functions, which differ only with boundary conditions, is available in Mathcad to make building the vector of second derivatives possible; cspline(vx,vy) generates the curve which is the cubical polynomial in boundary points; pspline(vx,vy) –respectively parabola; lspline(vx,vy) – straight line.

As an example, problem of interpolation of values of deflection of the beam at its length based on six initial values, obtained by solving the equation of structural mechanics is shown in the programme listing. Under the term of Extrapolation in Mathcad we understand foreseeing the behavior of function beyond the bounds of its definitional domain. In our case the problem is restricted to defining of the values of a certain parameter beyond the domain, in which the values of the given parameter are known. Among the closest to the right boundary points, which form the basis of extrapolation in Mathcad, n is the quantity of points in which extrapolation of data is realized. Results obtained in compliance with the function predict(v,m,n) to the large depend on parameter m. In programme listing you can see the results of function operation based on data on production output for the period of 12 months. 