interpolation-approximation

# 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 requirements 4. **Error Analysis**: Bound approximation errors rigorously ## Tools/Libraries - Chebfun - scipy.interpolate