Function interpolation and approximation methods
name interpolation-approximation description Function interpolation and approximation methods allowed-tools ["Bash","Read","Write","Edit","Glob","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