We may know the value of a function f at a set of points x1, x2, ..., xN. How do we estimate the value of the function at any point x*; how do we compute f(x*). This can be achieved by finding a smooth curve that passes though the points (x1, f(x1)), (x2, f(x2)), ... (xN, f(xN)). Alternatively, the points may be joined in sebintervals of [x1,xN] by piecewise . A third method is that of defining a straight line (or a polynomial of low degree) that is the best fit to the set of points.

Tutorial on Approximation

Polynomial Interpolation can be carried out using a method called Newton's Divided Difference Method.

Tutorial on Polynomial Interpolation : Polynomial Interpolation - Spreadsheet Demonstration

Tutorial on Piecewise Polynomial Interpolation

Tutorial on Basis Functions

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