Before revision:  For random TLSE problems , numerical experiments illustrate the sharpness of the estimates based on normwise condition numbers , while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
After revision:  For random TLSE problems , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution , while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.