This search of Google news, shows far more examples of "to my understanding" by itself, than of "according to my understanding", but that shouldn't stop you from using the latter. Both are idiomatic and familiar.
This search for "to my knowledge" gets 625 hits. While "as far as I know" shows about 1000 hits - which is about the limit (I believe) of the number of hits that Google will show, even when it gets more.
The difference in meaning is that usually "knowledge" refers to matters of fact:
As far as I know, all four are acceptable English.
while "understanding" refers to matters of interpretation or comprehension:
According to my understanding, the references to knowledge have a meaning different from the references to understanding.
I do not think, however, that this distinction is always made. For more examples of their usage in context, see the Google results above.