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Session 6
Numerical Methods

Polynomial Interpolation and Approximation

4 hours
Duration
8
Materials
6
Objectives
Session Overview

Comprehensive study of polynomial interpolation including Lagrange interpolation, Newton divided differences, Hermite interpolation, and error analysis. Chebyshev polynomials and optimal approximation.

Learning Objectives
By the end of this session, you should be able to:
  • Master Lagrange interpolation formula and its computational implementation
  • Understand Newton divided differences and forward/backward difference formulas
  • Implement Hermite interpolation for functions with derivative information
  • Analyze interpolation error using Weierstrass approximation theorem
  • Apply Chebyshev polynomials for optimal node placement and minimax approximation
  • Understand Runge phenomenon and strategies to avoid oscillations
Course Materials
Download materials for offline study and reference
Complete Interpolation Theory (50 pages)
Available material
Lagrange and Newton Method Implementations
Available material
Hermite Interpolation with Applications
Available material
Chebyshev Polynomials and Optimal Approximation
Available material
Error Analysis and Runge Phenomenon Study
Available material
Polynomial Approximation Project
Available material
Interactive Interpolation Visualization Tools
Available material
Real Data Approximation Examples
Available material