 On the other hand, the Gram–Schmidt process produces the formula_45th orthogonalized vector after the formula_45th iteration, while orthogonalization using Householder reflections produces all the vectors only at the end.This makes only the Gram–Schmidt process applicable for iterative methods like the Arnoldi iteration.Yet another alternative is motivated by the use of Cholesky decomposition for inverting the matrix of the normal equations in linear least squares.