Sensitivity analyses for factorizations of sparse or structured matrices
The effect of perturbations to a given matrix on the condition numbers of its QR, Choleskey, and related factorization is discussed. For the QR factorization, the authors give a practical example of structure in both the original matrix and perturbation matrices where the value of the new expression for the condition number is never greater than that of the old expression, and show that it is much smaller with particular values. For the Choleskey factorization they closely examine the case where both the original and perturbation matrices are symmetric and tridiagonal, and show that while the value of the new expression for the condition number is always bounded above by that for the old one, the difference can not be significant.
scientific article; zbMATH DE number 1371006