Incomplete LU factorization

Hmmm, okay, let me try to explain Incomplete LU Factorization in a way that a 5-year-old would understand.

So, you know how sometimes we have to solve math problems that are really big and have lots of numbers in them? Well, Incomplete LU Factorization is like a special trick that helps us solve those big problems faster and easier.

Imagine you have a big puzzle with lots of pieces that you need to put together. But, some of the pieces are missing and you don't know what they look like. In Incomplete LU Factorization, we try to put together as many pieces as we can by breaking up the big puzzle into smaller pieces that are easier to work with.

First, we try to divide the big puzzle into two smaller puzzles. One puzzle is called L and the other puzzle is called U. The L puzzle has lots of little pieces on the bottom left side, and the U puzzle has lots of little pieces on the top right side.

Once we have these two smaller puzzles, we try to solve them one at a time. We use some special math tricks to figure out what the missing pieces should be, and put them in their right places.

When we have solved both of these smaller puzzles, we can put them back together to get the answer for the big puzzle. And just like that, we have solved a big math problem really quickly and easily!

So, that's what Incomplete LU Factorization is all about. It's a special trick that helps us solve big math problems faster and easier by breaking them up into smaller puzzles and putting the missing pieces in their right places.