We introduce a new method for the calculation of bounds on the eigenvalues of Hessian matrices of twice continuously differentiable functions. Eigenvalue bounds of Hessian matrices arise in a number of notoriously difficult tasks in computational chemical engineering. For example, Hessian matrix eigenvalue bounds are used in global nonlinear optimization, global convexity/concavity analysis in ...

A choice test revealed that Hessian fly, Mayetiola destructor (Say) (Diptera: Cecidomyiidae), adults deposited approximately 3 times more eggs on wheat (Triticum spp.), seedlings than on barley (Hordeum spp.) or rice, Oryza sativa L., seedlings. On a barley seedling, 49.4% of eggs were deposited on either the abaxial leaf surface or the coleoptile and first leaf sheath (C&FLS), where newly hatc...

A fundamental computational procedure in practically all areas of scientific computing is the calculation of the Newton step (in n-dimensions). In many cases this computation represents the dominant cost in the overall computing task. Typically the Newton step computation breaks down into two separable subtasks: calculation of the Jacobian (or Hessian) matrix along with the right-hand-side, and...

A selfsimilar manifold is a Riemannian (M,g) endowed with homothetic vector field ξ. We characterize global manifolds and describe the structure of local manifolds. prove that any potential conical or Euclidean space. radiant Hessian (M,∇,g,ξ) such ∇ξ=λId, where λ constant. locally isomorphic to product

Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss ...