A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L ∞-norm

The ith singular value of a transfer matrix, σ_i(H(jω)), need not be a differential function of ω at frequencies where its multiplicity is greater than one. However, near a local maximum the largest singular value σ₁(H(jω)) has a Lipschitz second derivative, but need not have a third derivative. On the basis of this regularity result, the authors obtain a quadratically convergent algorithm for computing the L_∞-norm of a transfer matrix