Function interpolation and approximation methods
Scanned 9/2/2026
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---
name: interpolation-approximation
description: Function interpolation and approximation methods
allowed-tools:
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metadata:
specialization: mathematics
domain: science
category: numerical-analysis
phase: 6
graph:
domains: [domain:mathematics]
specializations: [specialization:computational-mathematics]
skillAreas: [skill-area:mathematical-reasoning, skill-area:statistical-analysis, skill-area:dynamic-programming]
workflows: [workflow:experiment-design]
roles: [role:computational-scientist, role:research-engineer]
---
# 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
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