Interpolation and Approximation Purpose Provides function interpolation and approximation methods for data fitting and function representation. Capabilities - Polynomial interpolation (Lagrange, Newton, Chebyshev) - Spline interpolation (cubic, B-spline) - Rational approximation (Pade) - Least squares fitting - Minimax approximation (Remez algorithm) - Approximation error bounds Usage Guidelines 1. Method Selection : Choose based on smoothness and accuracy needs 2. Node Placement : Use Chebyshev nodes to minimize Runge phenomenon 3. Spline Order : Select spline degree based on continuity requ…