Interpolation and Curve-fitting

Interpolation and curve-fitting both deal with fitting lists curves to a list of distrete points but there are some key differences in terminology:

Interpolation seeks a curve that

• Goes through all the points in the inputs.

• Assumes there is no measurement error in data points

• No ambiguity in mapping x and y (no duplicate y’s for a given x)

• Often used to capture the local behaviour

Curve fitting seeks a curve that

• is the best fit for all datapoints (in some sense)

• doesn’t necessarily traverse all the datapoints

• permits ambiguity in x-y pairs

• Is more of a global encapsulation of the data.

• generally recovers interpolation as a ‘perfect fit’ under the interpolation criteria.