What is a good Gram-Schmidt algorithm?

Question

There are so many different methods. Would like to see which ones have worked for many seasoned mathematicians here.

Answer 1

Modified Gram-Schmidt algorithm
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A is m x n, with m ≥ n s.t. rank(A) = n

(a) For i = 1, ... , n
`````````w_i = a_i
End (a) For
(b) For i = 1, ... , n
`````````r_ii = ||w_i||
`````````q_i = (w_i)/(r_ii)
`````````(c) For j = i + 1, ... , n
``````````````````r_ij =
``````````````````w_j = w_j - (r_ij)(q_i)
`````````End (c) For
End (b) For

Answer 2

http://en.wikipedia.org/wiki/Gram-Schmidt_algorithm