New rigorous perturbation bounds for the Cholesky-like factorization of skew-symmetric matrix

Some new rigorous perturbation bounds for the Cholesky-like factorization of skew-symmetric matrix are obtained when the original matrix has the normwise or componentwise perturbations, where the componentwise perturbation has the form of backward rounding error for the Cholesky-like factorization algorithm. These bounds can be much tighter than the existing one. Two numerical examples are provided to illustrate these results.