The notion of a low rank update arises in many important applications. This paper deals with the inverse problem of updating a rectangular matrix by additive low rank matrices so as to reposition the associated singular values. The setting is analogous to the classical pole assignment problem where eigenvalues of a square matrix are relocated. Precise and easy-to-check necessary and sufficient ...

Report Date: Written Language: Any Other Identifying Information of this Report: Distribution Statement: Supplementary Notes: The University of Aizu Aizu-Wakamatsu Fukushima 965-8580 Japan 10/22/2014 English First Issue: 10 copies Kazuya Matsumoto, Naohito Nakasato, and Stanislav Sedukhin Implementing Level-3 BLAS Routines in OpenCL on Different Processing Units Level-3 BLAS, GPU, multi-core CP...

‎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 $k$‎.

Historical Development of the BFGS Secant Method and Its Characterization Properties by Joanna Maria Papakonstantinou The BFGS secant method is the preferred secant method for finite-dimensional unconstrained optimization. The first part of this research consists of recounting the historical development of secant methods in general and the BFGS secant method in particular. Many people believe t...

The symmetric rank-one update method is well-known in optimization for its applications in the quasi-Newton algorithm. In particular, Conn, Gould, and Toint proved in 1991 that the matrix sequence resulting from this method approximates the Hessian of the minimized function. Extending their idea, we prove that the symmetric rank-one update algorithm can be used to approximate any sequence of sy...

Increasing the number of peers in a peer-to-peer network usually increases the number of answers to a given query as well. While having more answers is nice in principle, users are not interested in arbitrarily large and unordered answer sets, but rather in a small set of ”best” answers. Inspired by the success of ranking algorithms in Web search engine and top-k query evaluation algorithms in ...

In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...

A transversal of a hypergraph is a set of vertices intersecting each hyperedge. We design and analyze new exponential-time algorithms to enumerate all inclusion-minimal transversals of a hypergraph. For each fixed k ≥ 3, our algorithms for hypergraphs of rank k, where the rank is the maximum size of a hyperedge, outperform the previous best. This also implies improved upper bounds on the maximu...