PLU decomposition of a matrix

In the next part of the lecture, we will show how we can implement $ PLU $ factorization and how to write it efficiently.

from IPython.lib.display import YouTubeVideo
vid = YouTubeVideo("1Vqs28nmyoI")
display(vid)

Task

1. Now consider how to implement the $ PLU $ factorization of the $ A $ matrix.
2. After going through this lecture, go back to the previous one! There is inserted the code for solving three-diagonal systems which we apply to solving the differential equation

1. Some special types of linear systems

We observe $ A $ special structures, we are specifically interested in positive definite matrices and among them we are especially interested in those that are symmetric

from IPython.lib.display import YouTubeVideo
vid = YouTubeVideo("W-EzXWlJJjs")
display(vid)

Cholesky factorization

from IPython.lib.display import YouTubeVideo
vid = YouTubeVideo("NbA6MrtJ0kE")
display(vid)