A note on the error analysis of classical Gram-Schmidt (Q857865)

The authors consider the factorization of a full rank matrix \(A\) into \(A=QR\), where \(Q\) is a matrix of orthonormal columns and \(R\) is upper triangular. It is shown that the computed \(R\) satisfies \(R^T R=S^TA+E\), where \(E\) is a small backward error if the diagonals of \(R\) are computed in way similar to Cholesky factorization of the normal equations matrix. The authors end the paper on the implications of the results for the classical Gram-Schmidt reorthogonalization.