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LU Decomposition with Full Pivoting

This repository contains a Python script for performing LU decomposition on a given matrix with complete pivoting. LU decomposition is a method of factorizing a matrix into a product of a lower triangular matrix (L) and an upper triangular matrix (U). Full pivoting involves row and column interchanges to optimize the decomposition further.

Usage

  1. Run the script and choose the input mode:

    • File: Load matrix from a file.
    • Input: Manually input matrix elements.
    • Default Matrix: Use a predefined 3x3 matrix.

  2. Choose the decomposition method:

    • Without Economic Storage: Decompose the matrix without optimizing storage.
    • With Economic Storage: Optimize storage during decomposition.

  3. View or Save Results:

    • View the results in the terminal.
    • Save the results to an output.txt file.

Example

python LU-Full-Pivoting-Decomposition.py