scholarly journals Well-solvable cases of the QAP with block-structured matrices

2015 ◽  
Vol 186 ◽  
pp. 56-65 ◽  
Author(s):  
Eranda Çela ◽  
Vladimir G. Deineko ◽  
Gerhard J. Woeginger
2016 ◽  
Vol 2016 ◽  
pp. 1-3 ◽  
Author(s):  
Hal Caswell ◽  
Silke F. van Daalen

The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of whether the blocks are of the same or of different sizes.


2018 ◽  
Vol 34 ◽  
pp. 170-190 ◽  
Author(s):  
Sally Hill ◽  
Matthew Lettington ◽  
Karl Michael Schmidt

An equivalent representation of constant sum matrices in terms of block-structured matrices is given in this paper. This provides an easy way of constructing all constant sum matrices, including those with further symmetry properties. The block representation gives a convenient description of the dihedral equivalence of such matrices. It is also shown how it can be used to study their spectral properties, giving explicit formulae for eigenvalues and eigenvectors in special situations, as well as for quasi-inverses when these exist.


1981 ◽  
Vol 4 (4) ◽  
pp. 975-995
Author(s):  
Andrzej Szałas

A language is considered in which the reader can express such properties of block-structured programs with recursive functions as correctness and partial correctness. The semantics of this language is fully described by a set of schemes of axioms and inference rules. The completeness theorem and the soundness theorem for this axiomatization are proved.


Author(s):  
Weiqun Zhang ◽  
Andrew Myers ◽  
Kevin Gott ◽  
Ann Almgren ◽  
John Bell

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.


Sign in / Sign up

Export Citation Format

Share Document