Built into Mathematica are state-of-the-art constrained nonlinear fitting capabilities, conveniently accessed with models given directly in symbolic form. Mathematica also supports unique symbolic interpolating functions that can immediately be used throughout the system to efficiently represent approximate numerical functions.
FindFit — find a general nonlinear fit, potentially including parameter constraints
Fit — linear least-squares fit to a list of symbolic functions
LeastSquares — solution to a least-squares problem in matrix form
Interpolation — find an interpolation to data in any number of dimensions
InterpolatingFunction — represent an approximate function to be evaluated repeatedly
InterpolatingPolynomial — construct a symbolic interpolating polynomial