When nonlinear behavior must be considered in sensitivity analysis studies, one needs to approximate higher order derivatives of the response of interest with respect to all input data. This paper presents an application of a general reduced order method to constructing higher order derivatives of response of interest with respect to all input data. In particular, we apply the method to constru...

Notation. K will always denote a number eld. xI. Ranks of Families of Elliptic Curves For our purposes, a family of elliptic curves will be given by an equation E : y 2 = x 3 + A(T)x + B(T); A(T); B(T) 2 KT]; (T) = 4A(T) 3 + 27B(T) 2 6 = 0: We will always assume that E is non-split (i.e., is not obtained by base extension from a curve deened over K). The rank Generic Rank = Rank E(K(T)) is the ...

A new quasi-Newton scheme for updating a low rank positive semi-definite Hessian approximation is described, primarily for use in sequential quadratic programming methods for nonlinear programming. Where possible the symmetric rank one update formula is used, but when this is not possible a new rank two update is used, which is not in the Broyden family, although invariance under linear transfo...

In this paper I propose B-Rank, an efficient ranking algorithm for recommender systems. B-Rank is based on a random walk model on hypergraphs. Depending on the setup, B-Rank outperforms other state of the art algorithms in terms of precision, recall ∼ (19%− 50%) and inter list diversity ∼ (20%− 60%). B-Rank captures well the difference between popular and niche objects. The proposed algorithm p...

A new family of limited-memory variable metric or quasi-Newton methods for unconstrained minimization is given. The methods are based on a positive definite inverse Hessian approximation in the form of the sum of identity matrix and two low rank matrices, obtained by the standard scaled Broyden class update. To reduce the rank of matrices, various projections are used. Numerical experience is e...

In this paper we study a generalization of Kruskal’s permutation lemma to partitioned matrices. We define the k’-rank of partitioned matrices as a generalization of the k-rank of matrices. We derive a lower-bound on the k’-rank of Khatri–Rao products of partitioned matrices. We prove that Khatri–Rao products of partitioned matrices are generically full column rank.