Gaussian Elimination with Partial Pivoting

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• numericalmethodsguy

[sakkarugzo]

Question: Don't you need to divide each rows by the highest number in that row before you choose which row is the pivot? My professor warned us to make sure we do this division. I am confused only with this the rest is explained very clearly in your video. Thanks.

[numericalmethodsguy]

@sakkarugzo Although, not wrong, the division is not part of the algorithm. However such division would simply increase the computation time. Note that a division may take 16 clock cycles of time. I will soon write a blog on this topic.

[registerrajesh]

Hi, if element a11 and a21 are same then what to do for switching the rows? and element a11 and a21 have highest value then element a31?

[numericalmethodsguy]

@registerrajesh It all depends on how the maximum is found. If the algorithm has the condition written as "if max<=a(i,j) then max=a(i,j)", then row 2 and row 1 would get switched. If the algorithm has the condition written as "if max<a(i,j) then max=a(i,j)", then row 1 and row 1 would get switched.

[naveed017]

well explained...thank you

[pranab1234]

@sakkarugzo Is that not scaled partial pivoting that you are talking about? It is slightly different than partial pivoting, as you have already mentioned it.

[redsox09544]

thanks so much. the writing on the screen while explaining really helps!

[BlitzKiller4]

Thanks for teaching how to do the partial pivoting..... now I have to put it in MATLAB code......

[mojtabasadri]

Thank you so much sir.

It was really helpful.