name: interpolation-approximation description: Function interpolation and approximation methods allowed-tools:
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- Grep metadata: specialization: mathematics domain: science category: numerical-analysis phase: 6
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
- Method Selection: Choose based on smoothness and accuracy needs
- Node Placement: Use Chebyshev nodes to minimize Runge phenomenon
- Spline Order: Select spline degree based on continuity requirements
- Error Analysis: Bound approximation errors rigorously
Tools/Libraries
- Chebfun
- scipy.interpolate