Exponential splittings of products of matrices and accurately computing singular values of long products
The authors discuss the influence of perturbations \(E_i\) in the factors of long products \(A_n \cdots A_1\) of matrices on the relative error of the singular values of such products. This relative errors can be quite large in general. But as it is shown in the paper, the error in the singular values is \({\mathcal O}(n^2 \max_i \kappa_2(A_i) \|E_i\|_F)\) if the product has an exponential splitting. Numerical examples illustrating the behaviour of the relative errors in the singular values are presented.
scientific article; zbMATH DE number 1443449