On the sensitivity of the LU factorization
The paper presents how \(L\) and \(U\) change as \(A\) changes in the factorization \(A= LU\). The first-order perturbation results are derived in two ways. The so-called matrix-vector equation approach is used to provide sharp bounds, resulting in the condition numbers for the \(L\) and \(U\) factors, while the so-called matrix equation approach is used to obtain more practical bounds, resulting in easily computable upper bounds on the condition numbers. The effect of partial pivoting and complete pivoting on the sensitivity of the \(LU\)-factorization is presented and numerical results are given to illustrate the theoretical analysis.
scientific article; zbMATH DE number 1228550