Least Squares Curve Fitting for Arbitrary Combinations of Basis Functions

This source program performs least squares curve fitting for arbitrary combinations of basis functions. The implementation builds upon polynomial fitting algorithms, utilizing the least squares method to compute function coefficients that minimize approximation errors. The algorithm works by constructing a design matrix from the chosen basis functions and solving the normal equations through matrix operations. To enhance code readability, we have included comprehensive comments explaining the purpose and methodology behind each computational step. The program incorporates adjustable parameters allowing users to customize the fitting process according to their specific requirements. These parameters include tolerance settings for convergence criteria and options for handling numerical stability. We recommend that users possess fundamental mathematics knowledge (particularly linear algebra) and basic programming understanding to effectively utilize and interpret the program's output. The implementation employs key numerical computing techniques such as QR decomposition or singular value decomposition to ensure robust coefficient calculation.