- Improved computerized computation of Hessian matrix spectral bounds(arXiv)
Writer : Moritz Schulze Darup, Martin Mönnigmann
Summary : This paper presents a quick and highly effective technique for the computation of eigenvalue bounds for Hessian matrices ∇2φ(x) of nonlinear capabilities φ:U⊆Rn→R on hyperrectangles B⊂U. The strategy relies on a just lately proposed process for an environment friendly computation of spectral bounds utilizing prolonged codelists. Each the earlier method and the one introduced right here considerably differ from established strategies in that they do intentionally not use any interval matrices and thus end in a good numerical complexity of order O(n)N(φ), the place N(φ) denotes the variety of operations wanted to judge φ at a degree in its area. We enhance the earlier technique by exploiting sparsity, which naturally arises within the underlying codelists.
