Perturbation bounds for matrix square roots and Pythagorean sums
Let \(A\) be an \(n\times n\) complex matrix and let \(R\) be its square root (when such exists) while \(P=(I+A)^{1/2}\) denotes the Pythagorean sum. The author obtains perturbation estimates for \(R\) and \(P\). Further when the latter are accretive he obtains bounds for the solution of the matrix Sylvester equation and for the separation of two matrices.
scientific article; zbMATH DE number 69530
scientific article