I don't quite get this example of passing rows. I understand that the last row from a prior section and the first row from the next section is required to complete computation. However, does the row from the prior section not depend on any computed value from the current section?

@huangda - You are correct. This about this computation happening in phases.

1. Processors communicate their row data to their neighbors. So P1 sends datas to P2, and P2 sends data to P1.
2. Processors update their local elements based on the data they have. (This update includes update of the first row and last row they "own".)
3. Processors communicate their [updated] row data to their neighbors.
4. Processors update their local elements based on the data they have. (this update includes update of the first row and last row they "own") etc.