Skip to content

README.md

Latest commit

 

History

History
33 lines (27 loc) · 1.46 KB

README.md

File metadata and controls

33 lines (27 loc) · 1.46 KB

Numerical Optimization & Root-Finding Algorithms

Python · NumPy · SciPy · Scientific Computing · University of Toronto

Overview

Implementation and analysis of core numerical methods for root-finding, optimization, and constrained problems — validated against NumPy/SciPy library routines.

Methods Implemented

Notebook Method Category
01_root_finding Bisection, Newton's, Secant Root-Finding
02_fixed_point_iteration Fixed-Point Iteration, Convergence Analysis Root-Finding
03_optimization Golden Section, Newton's, Parabolic Interpolation Optimization
04_linear_programming Feasible Region, Vertex Evaluation Linear Programming
05_lagrange_multipliers Lagrange Multipliers, Hessian, SLSQP Constrained Optimization

Key Results

  • Bisection, Newton's, and Secant methods validated against SciPy fsolve
  • Convergence rates confirmed for fixed-point iteration schemes
  • Optimization minima matched SciPy minimize_scalar results
  • Lagrange multiplier solution matched SciPy minimize (SLSQP) results

Tools & Technologies

  • Language: Python 3.9
  • Libraries: NumPy, SciPy, Matplotlib
  • Methods: Root-Finding, Fixed-Point Iteration, Gradient-Based Optimization, Linear Programming, Constrained Optimization

Academic Context

Completed as part of CSC338 — Numerical Methods, University of Toronto, Winter 2025. All implementations are original work.