Solving-System-Linear-EQs

I developed these algorithms to solve linear equations using two methods: 1. gauss-seidel 2. Jacobi

This was done for CS 3010 Numerical Methods

Description:

Gauss-Seidel method: This is an itterative method used to solve a system of linear equations

Jacobi method: This is also an itterative method used to solve a system of linear equations.

Specifications:

These methods are very similar to each other with minor difference.

Both methods will run 50 times maximum.

There are 3 equations total and they are hard coded.

How:

There are couple of checks that need to be done before we begin:

Writing equations on top of each other there must be no zero terms along the diagonal if there are rearange the equations.
Solve each equation for x_i starting from i = 1. so the first equation is in terms of X₁ and so on.
start from an initial guess. here my initial values are all zeros: x₁ = 0 , x₂ = 0 , x₃ = 0

Jacobi :

use the initial guess to find x_i for all there equations
replace the x_i answers in a vector and use the found answers as the input guess for the next itteration.
repeat 50 times

Gauss-Seidel:

This method is almost exactly the same in the first step. find the first equation's answers based on initial guess.
Immedietly substitute the answer for x₁ into the vector to use for x₂.
Immedietly substitute the answer for x₂ into the vector to use for x₃
repeat these steps 50 times.

Used:

Java
No helping packages or implementations