Should we add Vector Sanitizers to Gram-Schmidt process

Hi there,

The problem:
I often do run into the situation that I want to orthogonalize a bunch of vectors which are in a subspace of the full FEM space. For example, vectors having mean value zero. As a second example, in the method "ArbiLoMod", we have vectors wherein one part (the "extension") is calculated by applying a linear operator to another part.
Often, this property deteriorates during the Gram-Schmidt process: When one starts with nearly linear dependent vectors, numerical noise is amplified during the Gram-Schmidt process. This numerical noise is not in the subspace and the resulting vector is not in the subspace.

The solution:
I would suggest to add an optional option "sanitizer" to the Gram-Schmidt process, which is a callable which brings the vectors back into the subspace. The Gram-Schmidt algorithm should apply this sanitizer after steps which amplify numerical noise.

What are your opinions?

The issue names the Gram-Schmidt process and the ArbiLoMod vector relationship, but no file, test, or entry point. Locate the Gram-Schmidt implementation, determine where numerical noise is amplified, and clarify how an optional sanitizer should be applied; done means the behavior and expected subspace-preserving results are specified and tested.