Ok.. after some digging i cam across a paper (Henderson, 1981) on deriving the inverse of a matrix sum:
Which in my case simplifies to:
now i can calculate my inverse C just once and seems to be giving me the same results... although i'm sill having to calculate a different inverse in each iteration, so not a complete solution...
I found another similar method (Miller, 1981) which seems to over come this problem but it requires one of the matrices to be rank 1, which neither C nor aI(j) is.
so still a bit stuck.