Data

1. Introduction to Interpolation
• Definition of interpolation
• Importance in numerical analysis
• Used to estimate unknown values

2. Applications of Interpolation
• Engineering and science
• Computer graphics
• Data prediction
• Signal processing

3. Types of Interpolation Methods
• Linear interpolation
• Polynomial interpolation
• Spline interpolation
• Lagrange interpolation

4. Linear Interpolation
• Simplest method
• Assumes linearity between two points
• Equation: y = y0 + (x-x0)*(y1-y0)/(x1-x0)

5. Polynomial Interpolation
• Fits an nth degree polynomial
• Can pass through multiple data points
• Risk of Runge’s phenomenon

6. Lagrange Interpolation
• Uses Lagrange basis polynomials
• Constructs a polynomial passing through all
data points
• Widely used in numerical methods

7. Spline Interpolation
• Piecewise polynomial functions
• Cubic splines are common
• Ensures smoothness at data points

8. Advantages of Interpolation
• Accurate estimation within known data range
• Useful in curve fitting
• Applicable to various domains

9. Limitations of Interpolation
• Accuracy decreases outside data range
(extrapolation)
• High-degree polynomials may oscillate
• Requires careful method selection

10. Conclusion
• Interpolation is a key numerical tool
• Different methods suit different applications
• Important in data analysis and engineering