Survey of methods of numerical approximation

The problem of fitting a curve, or series of curves, to data occurs frequently in all branches of the physical, biological and social sciences. The data may have been obtained experimentally or may be given by the values taken by a complicated function at specified points. If the data have been obtained experimentally they may be subject to experimental errors and this may have to be taken into account in our choice of curve; if the data have been obtained from the values of a known but complicated function our objective may be to find a simpler function of some particular type which fits the data to within some specified accuracy over a finite range. The author considers the two-dimensional problem; this is important in itself and also provides the basis for extension to three (or more) dimensions. (12 refs).