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Session 3
Numerical Methods
Root Finding Methods: Open Methods
3.5 hours
Duration
7
Materials
6
Objectives
Session Overview
Advanced root finding techniques including Newton-Raphson method, secant method, and modified Newton methods. Analysis of convergence, multiple roots, and computational complexity.
Learning Objectives
By the end of this session, you should be able to:
- Derive and implement Newton-Raphson method with geometric interpretation
- Master the secant method and understand its superlinear convergence
- Handle multiple roots using modified Newton methods
- Analyze quadratic convergence of Newton method and linear convergence of secant method
- Implement deflation techniques for polynomial root finding
- Compare open methods with bracketing methods for various function types
Course Materials
Download materials for offline study and reference
Mathematical Derivations and Proofs (35 pages)
Available material
Newton Method Convergence Analysis
Available material
Secant Method Implementation Guide
Available material
Modified Newton Methods for Multiple Roots
Available material
Comparative Performance Study
Available material
Programming Project: Complete Root Finder Package
Available material
Real-world Application Examples
Available material