The BFGS update and the DFP update perhaps are respectively the most successful Hessian and inverse Hessian approximations for unconstrained minimization problems This paper describes a geometric meaning of these updates understood from the Wedderburn rank one reduction formula

We consider the online list accessing problem and present a new family of competitive-optimal deterministic list update algorithms which is the largest class of such algorithms known to-date. This family, called Sort-by-Rank (sbr), is parametrized with a real 0 1, where sbr(0) is the Move-to-Front algorithm and sbr(1) is equivalent to the Timestamp algorithm. The behaviour of sbr() mediates bet...

‎three infinite families of finite abelian groups will be‎ ‎described such that each member of these families has‎ ‎the r'edei $k$-property for many non-trivial values of $k$‎.

llc is a language based on C where parallelism is expressed using compiler directives. The llc compiler produces MPI code which can be ported to both shared and distributed memory systems. In this work we focus our attention in the llc implementation of the Workqueuing Model. This model is an extension of the OpenMP standard that allows an elegant implementation of irregular parallelism. We eva...

Abstract. We consider the task of updating a matrix function f(A) when the matrix A ∈ Cn×n is subject to a low-rank modification. In other words, we aim at approximating f(A+D)− f(A) for a matrix D of rank k n. The approach proposed in this paper attains efficiency by projecting onto tensorized Krylov subspaces produced by matrix-vector multiplications with A and A∗. We prove the approximations...

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...