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interpolation-approximation

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Function interpolation and approximation methods

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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