What is exactly pivoting ( in Gaussian elimination)?

[XodoX]

In terms of programming. Like, let's say you have F1+F2+F3+15=0 and you move the 15 to the other side, just as you're supposed to, which would be F1+F2+F3= -15. Is that what they mean by pivoting? The code moves the 15?

thanks

 

[Stephen Tashi]

No. The "pivot" is a single entry in a row of a matrix. "Pivoting" refers to a process involving several steps. The row is divided by the value of the pivot to turn the pivot into 1. Then all the entries in the column of the pivot and directly below it are turned into zeroes by subtracting some multiple of the pivot's row from them.

If you're planning to write a serious program to solve linear equations, you should consult a text on numerical methods. The better numerical algorithms do not simply march down the main diagonal using each entry as a pivot.

 

[XodoX]

No. The "pivot" is a single entry in a row of a matrix. "Pivoting" refers to a process involving several steps. The row is divided by the value of the pivot to turn the pivot into 1. Then all the entries in the column of the pivot and directly below it are turned into zeroes by subtracting some multiple of the pivot's row from them.

If you're planning to write a serious program to solve linear equations, you should consult a text on numerical methods. The better numerical algorithms do not simply march down the main diagonal using each entry as a pivot.

Thanks. How would I call it then - to get each equation into the right format? I don't know how to program this, but I need it for reference for Gaussian elimination systems. It owuld be a nice tool to have. But usually they don't format the equations - at least the ones I could find online.

 

[Stephen Tashi]

How would I call it then - to get each equation into the right format?

What do you mean by "it"? Do you mean the example, you gave? What you did (as best I can determine) is not a process that has a distinctive name. You transformed the equation into one that has no constant on the left hand side.

I need it for reference for Gaussian elimination systems.

I can't tell whether you are merely interested in terminology for something or whether you want to know how to write a computer program to do Gaussian elimination.

 

[XodoX]

What do you mean by "it"? Do you mean the example, you gave? What you did (as best I can determine) is not a process that has a distinctive name. You transformed the equation into one that has no constant on the left hand side.




I can't tell whether you are merely interested in terminology for something or whether you want to know how to write a computer program to do Gaussian elimination.

I'd like to have a program for my Gaussian elimination equations, but the codes I found won't do F1+F2+F3+10=0 since the 10, in this case, has to be moved over to the right. I was wondering if someone knew where to get a code like this. I want to try it out.

 

[Stephen Tashi]

You shouldn't make up terminology like "Gaussian elimination systems" and "Gaussian elimination equations" without explaining what you mean.

I think what you're trying to say is that you would like a computer program that will solve a systems of equations by using Gaussian elimination. That still leaves questions unanswered.

You say you want "a code". Does this mean source code? If so, what computer language would you want this code to be in? Or do you want a program with a graphical interface where you can enter the equations and see the Gaussian elimination done step by step? Are you mainly interested in solving the equations or mainly interested in Gaussian elimination? (As I mentioned before, Gaussian elimination is usually not the best way to solve systems of equations. )