Overview of QUIC-SVD - UMass Graphics Lab - University of ...

Parallelize Gram Schmidt Orthogonalization
• Classical Gram Schmidt:
Assume v1 , v2, v3... vn
are in the current basis set (i.e. they
are orthonormal vectors), to add a new vector :
v
( , ) ( , ) ... ( , )
r
1
r where proj( r, v) ( r v)
v
r r proj r v1 proj r v2
proj r v n
n
• This is easy to parallelize (as each projection is independently
calculated), but it has poor numerical stability.
r
21