3. Lu Decomposition
LU DE-COMPOSITION IS ANOTHER METHOD TO SOLVE A SET
OF SIMULTANEOUS LINEAR EQUATION
IN ALGEBRA LINEAR, THE LU DE-COMPOSITION IS A MATRIX
DECOMPOSITION WHICH WRITES A MATRIX AS THE PRODUCT
OF A LOWER TRIANGULAR MATRIX AND AN UPPER
TRIANGULAR MATRIX
4. Method
FOR MOST NON-SINGULAR MATRIX [A] THAT ONE COULD
CONDUCT NAÏVE GAUSS ELIMINATION STEPS, ONE CAN ALWAYS
WRITE IT AS,
[A] = [L][U]
Where,
[L] = Lower Triangular Matrix
[H] = Higher Triangular Matrix
5. [A] to [L] and [U]
A = 1 0 0
l21 122 0
l31 l32 1
6. FLOWCHART TO SOLVE L-U
DECOMPOSITION PROBLEMS
AX=B
LUX=B
LZ=B (LET UX=Z)
FINDING Z FIRST CAUSE WE L AND B ARE KNOWN(CONSTANTS)
THEN EQUATING Z IN UX=Z CAUSE U IS KNOWN AND AT THIS POINT Z IS
KNOWN
FINDING X
Here L is lower triangular matrix
And U is upper triangular matrix
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Thank You All For
Attending
This Session
Have A Nice Day…!