I Completeness of a basis function

[member 428835]

No, sorry, it has been a while since I have done PDEs or worked with Green's function in general.

No worries, thanks for taking the time!

 

[FactChecker]

Not really, sorry. I am a bit confused; your new functions are linear combinations of the previous, so I don't see what you may gain from it. Why not keep the original basis and just use combinations of it?

It is often nice to represent a function in terms of a basis that gives a clean interpretation of the components in the specific current context. So there are reasons to convert from one basis to another, as appropriate.

 

[member 428835]

It is often nice to represent a function in terms of a basis that gives a clean interpretation of the components in the specific current context. So there are reasons to convert from one basis to another, as appropriate.

Yes, the input to the Ritz procedure I employ must satisfy all BCs. As is, the basis functions don't satisfy all the BCs. So we take linearly independent combinations of basis functions to form new basis functions such that the additional BC is satisfied.