I'm very beginner in numerical methods... I have the pseudo-code
(look at image), but I don't know how intrepret this and how
I can implement this in C++...
Factorization? Gram-Schmidt is for orthonormalizing a basis. Start with a (numbered) set of vectors. Take the first one, normalize it (divide it by it's length) then fix the remaining ones so that their scalar product with the first one is 0 (using the last formula in the picture). Repeat for the remaining vectors.
If unclear, the algorithm should be well explained in wikipedia.
It's an exercise for my college. I must parallelize the sequential Gram-Schmidt's algorithm and compare execution time of both version (of course for large matrix).