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I know what LU Decomposition is but I don't know why we have have to learn about it. What are we using it for? (What's the point to know about it?)

Thanks.

UnknownW
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    http://www.saylor.org/site/wp-content/uploads/2011/11/ME205-4.4-TEXT.pdf – Amzoti Jan 26 '14 at 20:08
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    What can you use LU decomposition for? (solving a system of equations) Why can't you just invert the matrix and multiply on the other side? (you certainly can but it takes longer). Also you can do LU decomposition in-place. Which is what Amzoti's link says. – Mitch Jan 26 '14 at 20:15
  • Thanks for your comments. The link of Amzoti was very useful. – UnknownW Jan 26 '14 at 22:33
  • $LU$ decomposition is the systematic way of doing Gauß elimination. – Lutz Lehmann Apr 09 '18 at 17:08

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The source for my answer is Richard C. Penney's Linear Algebra: Ideas and Applications, 4th edition.

LU decomposition is useful if you want to solve the matrix equation AX = Y for many different Ys with the same A because in that case, you need decompose A only once, and AX = LUX = Y can be solved without row reduction.

Another feature that makes LU decomposition numerically efficient is that as you reduce A to get U, you get L without any more work.

user0
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