Matrix equations

Project Description

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

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

Clone the repository:

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

Run the program:

go run cmd/gauss/main.go

go run cmd/householder/main.go