Is the Q wrong in our example 1 (with the combined P)?

SciML / PDERoadmap

A repository for the discussion of PDE tooling for scientific machine learning (SciML) and physics-informed machine learning

https://tutorials.sciml.ai/

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Is the Q wrong in our example 1 (with the combined P)? #17

Closed jlperla closed 6 years ago

jlperla commented 6 years ago

Basically, when performing the gaussian elimination, why didn't "r" enter any equations?

jlperla commented 6 years ago

Similar, see #19 for understanding why the drift/variance don't enter with the gaussian elimination.

For the P = r I - L example, it is true that we augment the r I part of the operator with one row of 0s, which would explain part of the reason it doesn't enter Q, but in the second row it does enter....

jlperla commented 6 years ago

I am going to close this. I did a test of solving the system, and it (indeed) was correct with no "r" in the Q matrix. The question remains, what sort of "Gaussian Elimination" process is making this magic happen.