360,378 research outputs found
Generalized Filtering Decomposition
This paper introduces a new preconditioning technique that is suitable for
matrices arising from the discretization of a system of PDEs on unstructured
grids. The preconditioner satisfies a so-called filtering property, which
ensures that the input matrix is identical with the preconditioner on a given
filtering vector. This vector is chosen to alleviate the effect of low
frequency modes on convergence and so decrease or eliminate the plateau which
is often observed in the convergence of iterative methods. In particular, the
paper presents a general approach that allows to ensure that the filtering
condition is satisfied in a matrix decomposition. The input matrix can have an
arbitrary sparse structure. Hence, it can be reordered using nested dissection,
to allow a parallel computation of the preconditioner and of the iterative
process
Distance-generalized Core Decomposition
The -core of a graph is defined as the maximal subgraph in which every
vertex is connected to at least other vertices within that subgraph. In
this work we introduce a distance-based generalization of the notion of
-core, which we refer to as the -core, i.e., the maximal subgraph in
which every vertex has at least other vertices at distance within
that subgraph. We study the properties of the -core showing that it
preserves many of the nice features of the classic core decomposition (e.g.,
its connection with the notion of distance-generalized chromatic number) and it
preserves its usefulness to speed-up or approximate distance-generalized
notions of dense structures, such as -club.
Computing the distance-generalized core decomposition over large networks is
intrinsically complex. However, by exploiting clever upper and lower bounds we
can partition the computation in a set of totally independent subcomputations,
opening the door to top-down exploration and to multithreading, and thus
achieving an efficient algorithm
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Combinational multiple-valued circuit design by generalised disjunctive decomposition
A design of multiple-valued circuits based on the multiple-valued programmable logic arrays (MV PLA’s) by generalized disjunctive decomposition is presented. Main subjects are 1) Generalized disjunctive decomposition of multiple-valued functions using multiple-terminal multiplevalued decision diagrams (MTMDD’s); 2) Realization of functions by MV PLA-based combinatorial circuits
Generalized decomposition and cross entropy methods for many-objective optimization
Decomposition-based algorithms for multi-objective
optimization problems have increased in popularity in the past decade. Although their convergence to the Pareto optimal front (PF) is in several instances superior to that of Pareto-based algorithms, the problem of selecting a way to distribute or guide these solutions in a high-dimensional space has not been explored. In this work, we introduce a novel concept which we call generalized
decomposition. Generalized decomposition provides a framework with which the decision maker (DM) can guide the underlying evolutionary algorithm toward specific regions of interest or the entire Pareto front with the desired distribution of Pareto optimal solutions. Additionally, it is shown that generalized decomposition simplifies many-objective problems by unifying the three performance objectives of multi-objective evolutionary algorithms – convergence to the PF, evenly distributed Pareto
optimal solutions and coverage of the entire front – to only one, that of convergence. A framework, established on generalized decomposition, and an estimation of distribution algorithm (EDA) based on low-order statistics, namely the cross-entropy method (CE), is created to illustrate the benefits of the proposed concept for many objective problems. This choice of EDA also enables
the test of the hypothesis that low-order statistics based EDAs can have comparable performance to more elaborate EDAs
Perturbative method for generalized spectral decompositions
Imposing analytic properties to states and observables we construct a
perturbative method to obtain a generalized biorthogonal system of eigenvalues
and eigenvectors for quantum unstable systems. A decay process can be described
using this generalized spectral decomposition, and the final generalized state
is obtained.Comment: 21 Page
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