LU Decomposition Method: Decomposing a Matrix Example: Part 2 of 2

Learn via an example how to take a square matrix [A] and decompose it into LU form.

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[arqi25]

Hi Sir, I understand what you did there, but how would you use LU decomposition to solve this problem [1 1 -1 ] [x1] [-1] 2 -1 1 x2 = 4 1 -1 -1 x3 1

sorry about the brackets they r supposed to be long! Thank You.



[numericalmethodsguy]

@arqi25 One would decompose the coefficient matrix the same way as the example. You decompose square matrices, not sets of equations. In this case A=[1 1 1; 2 -1 1 ; 4 1 -1], X=[x1, x2 x3], C=[-1 4 1]. First decompose A=LU, then solve LZ=C, and then UX=Z.

Go to numericalmethods(dot)eng(dot)u­sf(dot)edu; click Keyword. Click LU Decomposition. Read textbook chapter.

Go to numericalmethodsguy channel on YouTube, click playlists, click LU Decomposition & see the 2nd video.

[devinep5]

What if the matrix i am given equals something?

[numericalmethodsguy]

@devinep5 Give me the problem statement. Remember if AX=C is a set of eqns, the decomposition of A just depends on A, not on C.

[andronicusyyz]

So this was pretty good in explaining LU decomposition. However, what is the use of this in terms of solving a system of equations? Why would one use this method over alternatives such as Gauss-Jordan Inversion or Cramer's Rule?

[numericalmethodsguy]

@andronicusyyz It is all about computation time. LU Decomposition takes less computation time if you have to solve many sets of eqns with different RHS or if you are finding inverse of a matrix. Go to numericalmethods(dot)eng(dot)u­sf(dot)edu, and click on keyword, click on LU decomposition, annd see the textbook chapter, and go to page 2. You will have the complete answer!

[raffa123able]

very well set out, I appreciate this tutorial very much

[gelidusgaudium]

Thank you!

[TheDanydanial]

Thanks a lot..really helpful..now i know how to get L by just using the multiplier which can be got from U =)

[MetallicOrange]

Excellent! Extremely helpful!