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Sunday, 6 May 2018

Gauss Seidel, Gauss Elimination & Gauss Jordan - Whats the Difference?


Gauss-Seidel, Gauss Elimination & Gauss Jordan are the few of the most commonly used direct methods for obtaining a direct solution of linear equations. But, with such a common Nomenclature its rather difficult to determine which name relates to which method. Even I've felt myself getting confused on which name refers to which technique. So as a solution I devised the following mnemonic tool

Lets start with the First,

Gauss-Seidel

You see it kind of tells you that simultaneously iterate, the S and the I in the name Siedal. So this is the method that is based on iteration of equations to determine the final solution. In most common university questions you're asked to iterate upto four iterations and call the final solution as your answer.
  

Gauss Elimination

Now you see, it was just too difficult and time-consuming to solve too many equations and re-iterate them. Why not eliminate the steps and obtain the solution in an easy way.
Here comes the Matrix to our aid, you can convert the given system of equations into their matrix form and then simplify the matrix to an upper triangle or lower triangle which makes it easier to equate and solve the equations.
So let's remember it as Gauss Elimination - Eliminate the lower triangle of the matrix.
You can learn more about Gauss Elimination Method here

Finally the most waited!

Gauss Jordan

Gauss and Jordan are the names of two scientists or mathematicians that developed this technique. As you might have read the about the previous method, now you need to believe that most genius People aren't satisfied at all. They didn't want to back substitute the values after they solved the matrix and so decided why not make it more simply (I'd say they'd made it troublesome) by completing all the steps in the matrix itself. As a solution, they decided to convert the matrix into an identity matrix by simplifying the matrix. Once you have the identity matrix, the corresponding elements are the solutions of the required system of linear equations.
So let's remember it as Gauss Jordan - Small Names so make the matrix a unit matrix which is small as well




Much of that was made up stories just to remember the concepts and kick them into action whenever needed.

Thanks for Reading

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