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11

# Interpolation and Approximation

## 11.1 Interpolation

For practical use, it is convenient to have an analytical representation of the relationships between variables in a physical problem, and this representation can be approximately reproduced from data given by the problem. The purpose of such a representation might be to determine the values at intermediate points, to approximate an integral or derivative, or simply to represent the phenomena of interest in the form of a smooth or continuous function.

Interpolation refers to the problem of determining a function that exactly represents a collection of data. The most elementary type of interpolation consists of fitting a polynomial to a collection of data points. For numerical purposes, polynomials ...

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