Talk:Balanced Truncation

I prefer to add a wiki page for the cross Gramian approach and delete the direct truncation part (where does the name come from?) here. - U. Baur

OK with me. The source of the name I don't remember, I guess some talk, I have been using it for some time. It seems fitting, as without the balancing the truncation happens directly, thus my initial append of the BT article due to the close relation. - C. Himpe

I agree with U. Baur. This direct truncation is usually referred to as cross Gramian balanced truncation for which several extra research articles can be found. Hence, it should be called that way, or it should get a wiki page of its own. Either way some references are required. - P. Kürschner

Please add a reference that introduces / uses the term "Cross Gramian Balancing". Thanks. - C. Himpe

The only reference with the term "Cross Gramian Balancing" I was able to find is "Model reduction using semidefinite programming", which is touches the cross gramian topic with only 5 lines of text and cites a Sorensen paper from 2002 which uses the term "Approximate Balancing". I did find no reference to "Cross Gramian Balanced Truncation". In both cases I just might not have looked in right places. I personally would prefer a naming that focusses on the Truncation and not the Balancing, since there is no balancing procedure (as with WC and WO) involved, thus my usage of "Direct Truncation". - C. Himpe

The origin is exactly this Sorensen, Anthoulas paper. The term, approximate reduction is, however, commonly associated with approaches where the Gramians are in some way approximated. It does to my knowledge not refer to this particular approach. - P. Kürschner

To make it clearer, I think it is not bad to add some sentences like: The original system is directly truncated by the Cross Gramian approach without any balancing. The reduced model is thus not balanced. -L. Feng

+1 - C. Himpe

TODO: LQG-BT, BT 4 DAEs - P. Kürschner