Can anyone explain to me how to use LU factorization to solve Ax=b? I know how to solve for L and U, but using them to solve that confuses me. I'll post the question immediately.

Question

snowfire · Answer

attachment

snowfire · Answer

Just the first problem, I should be able to figure it out after that.

agent0smith · Answer

@zepdrix maybe?

anonymous · Answer

A=LU; Ax=B; LUx=B; x=inverse(U)inverse(L)B

snowfire · Answer

So is that what I want to do with them? Find their inverses and multiply that by B?

agent0smith · Answer

Looks like it, from this pic http://1.bp.blogspot.com/_ltmZpULxXtI/TDJf3yVx32I/AAAAAAAAAUs/rryzvfhJkpw/s1600/eq18.png

anonymous · Answer

it should be easier to find the inverse of a triangular matrix than a regular one

agent0smith · Answer

Just need the inverse of L, multiply that by matrix b, then it should be easy to solve the system.

snowfire · Answer

Okay makes sense, now to find the inverse, I augment the matrix to a similarly sized identity matrix, row reduce, and use the right half when the left half looks like the identity matrix right?

agent0smith · Answer

Yep, that sounds right.

snowfire · Answer

Alright, thanks you two! Would give you both a medal, but technically eashy answered first =P

agent0smith · Answer

He could prob use it more. Even though I can't see it, I think my smartscore is 99 already.

snowfire · Answer

It is, show off! ^^

agent0smith · Answer

Haha, thank you :P