Backend / AlgorithmsCompleted

Gauss Elimination

Gauss Elimination is an educational project that demonstrates the Gaussian elimination method in practice. The Python application solves linear systems by transforming matrices into row-echelon form and applying back-substitution. The repo includes the algorithm implementation, a random system generator and a CLI script to run computations on custom input. It also contains sample input files and explanations of the numerical concepts used.

Jan 2024 — Jan 2024

Tech Stack

Python

Key Features

  • Complete implementation of Gaussian elimination
  • Partial pivoting for improved numerical stability
  • Back-substitution routine
  • Handling of consistent, inconsistent and underdetermined systems
  • Random system generator for testing
  • Input file parsing for batch runs

Challenges

  • Ensuring numerical stability for small pivots
  • Handling inconsistent or underdetermined systems robustly
  • Providing clear, step-by-step matrix processing output
  • This project was one of the more demanding algorithmically and required substantial study of numerical methods

Solutions

  • Implemented partial pivoting to improve stability
  • Added input validation and explicit handling of edge cases
  • Designed a modular structure separating elimination, generation and parsing logic
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