Interpolation and Approximation

Abstract

Most engineering and scientific phenomena, such as the surface of a landscape or the continuously changing temperature at a location are inherently infinite in space or time or both. We cannot measure all the data. Generally it is possible to record surface elevation values or the temperature only at some specific locations and times.

However, it is possible to estimate the values at the unmeasured locations and times from the measured ones. This estimation can be done by interpolation or approximation. Both interpolation and approximation methods develop for the entire studied phenomena some interpolation functions, such as for temperature a temperature function and for the landscape elevation a surface function. Interpolation functions preserve the measured values, while approximation functions are more general, and they may not preserve the individual measured values. The interpolation and approximation functions are usually expressed by constraints, hence they can be conveniently represented in constraint databases.

Section 18.1 describes linear interpolation, which is used frequently to estimate the missing values of a partially known function.