I'm have a little trouble understanding PA=LU, I have no problems with A=LU but can't seem to figure out the Permutation matrix.(adsbygoogle = window.adsbygoogle || []).push({});

So I have summarised the process I am using let me know where it can be improved.

Step 1: Using Gaussian Elimination with partial pivoting reduce A to form a matrix U.

Step 2: The matrix L is formed by the "negative of the row reduction multiples" eg: R2=R2-(3/4)R3 then -(3/4) is an element in the the matrix L.

Now here is the first problem, as with the A=LU decomposition do these multiples remain fixed in place or do they also permute around depending on row interchanges ?

eg: say R2=R2-(3/4)R3 is the first operation than (-3/4) should go in the position of Row 2, Column 1. But, later if I need to interchange R2 with say R4 (for partial pivoting) will this effect the position of (-3/4) in the matrix L ?

Step 3: Now that you have matrix L and U, form the matrix P with the row interchanges during the process of pivoting.

For example: If during pivoting R1<->R4 and R4<->R3 than

[tex] \begin{bmatrix}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & 1 & 0\\

0 & 0 & 0 & 1

\end{bmatrix} [/tex]

becomes(R1<->R4)

[tex] \begin{bmatrix}

0& 0 & 0 & 1\\

0 & 1 & 0 & 0\\

0 & 0 & 1 & 0\\

1 & 0 & 0 & 0

\end{bmatrix} [/tex]

and finally (R4<->R3)

[tex]\begin{bmatrix}

0& 0 & 0 & 1\\

0 & 1 & 0 & 0\\

1 & 0 & 0 & 0\\

0 & 0 & 1 & 0

\end{bmatrix} [/tex]

The lecture notes I have are extremely complicated and involve L inverse theory which makes my head hurt and I can't find any useful resources online.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# PA=LU decomposition (w/ Partial Pivoting)

**Physics Forums | Science Articles, Homework Help, Discussion**