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.

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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.

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How:

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

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

Jacobi :

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

Gauss-Seidel:

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

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Used:

• Java
• No helping packages or implementations