Introduction to Interpolation
• Definition of interpolation
• Importance in numerical analysis
• Used to estimate unknown values
Applications of Interpolation
• Engineering and science
• Computer graphics
• Data prediction
• Signal processing
Types of Interpolation Methods
• Linear interpolation
• Polynomial interpolation
• Spline interpolation
• Lagrange interpolation
Linear Interpolation
• Simplest method
• Assumes linearity between two points
• Equation: y = y0 + (x-x0)*(y1-y0)/(x1-x0)
Polynomial Interpolation
• Fits an nth degree polynomial
• Can pass through multiple data points
• Risk of Runge’s phenomenon
Lagrange Interpolation
• Uses Lagrange basis polynomials
• Constructs a polynomial passing through all
data points
• Widely used in numerical methods
Spline Interpolation
• Piecewise polynomial functions
• Cubic splines are common
• Ensures smoothness at data points
Advantages of Interpolation
• Accurate estimation within known data range
• Useful in curve fitting
• Applicable to various domains
Limitations of Interpolation
• Accuracy decreases outside data range
(extrapolation)
• High-degree polynomials may oscillate
• Requires careful method selection
Conclusion
• Interpolation is a key numerical tool
• Different methods suit different applications
• Important in data analysis and engineering

Interpolation_Methods_data_analytics.pptx