We give a family of augmented systems as well as minimally extended systems 
which are suitable for the numerical detection and determination 
of singular points of Banach space problems. 
The systems are constructed in such a way 
that they only differ in a small part 
which must be adapted to the equivalence class 
to which the desired singular point belongs. 
The presented general results are specialized to the case of  
two-point boundary value problems.  
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