Matrix equations

Project Description

This program solves a system of linear equations using two methods:

1. Gauss method:
   It solves the system using the Gauss method with the choice of the leading element by row ans finds the inverse matrix.

2. Reflection (Householder) method:
   It decomposes the matrix into an orthogonal matrix (Q) and an upper triangular matrix (R) to solve the system via matrix factorization.

The system is represented by the equation:

$$A \cdot x = b$$

Where:

• The matrix A is defined as:

  $$a_{ii} = 5i,$$ $$a_{ij} = -(i + \sqrt{j}), \quad i \neq j,$$ $$i, j = 1, N, \quad N = 15.$$

• The vector b is defined as:

  $$b_i = 3\sqrt{i}, \quad i = 1, N.$$

The matrix A and vector b are created dynamically based on these formulas.

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Installation

1. Clone the repository:

   git clone git@github.com:LLIEPJIOK/matrix-equations.git 

2. Navigate to the project folder:

   cd matrix-equations 

3. Run the program:

   • Run Gauss method

   go run cmd/gauss/main.go  

   • Run Householder method

   go run cmd/householder/main.go