Interpolation is said to have no unique solution because, given only the requirement that a function pass through the data points, there exist infinitely many different functions that can satisfy this exact condition. The difficulty of the problem lies not in the existence of an interpolant, but in selecting among the many valid functions.
Conditions: A finite set of data points is given.; No extra constraints beyond passage through the points are imposed.
Interpolation is said to have no unique solution because, given only the requirement that a function pass through the data points, there exist infinitely many different functions that can satisfy this exact condition. The difficulty of the problem lies not in the existence of an interpolant, but in selecting among the many valid functions.
Conditions: A finite set of data points is given.; No extra constraints beyond passage through the points are imposed.