Can someone explain in details what every step in the modified gram Schmidt algorithm is doing?
This is what I think could someone correct me if I am wrong?
We are using a series of temporary vectors to build columns of Q and the non-zero elements of R. We iterate over the columns of A, completing a full run through of algorithm for each column of A. In modified GS instead of computing all the dot products from the original vectors, perform the projections one by one, using the result of the previous projections as the input to the next. By doing this we don't suffer from numerical instability as the round off errors in CGS can accumulate and destroy the orthogonality of the resulting vectors.