1,198 research outputs found
A complete closed-form solution to a tropical extremal problem
A multidimensional extremal problem in the idempotent algebra setting is
considered which consists in minimizing a nonlinear functional defined on a
finite-dimensional semimodule over an idempotent semifield. The problem
integrates two other known problems by combining their objective functions into
one general function and includes these problems as particular cases. A new
solution approach is proposed based on the analysis of linear inequalities and
spectral properties of matrices. The approach offers a comprehensive solution
to the problem in a closed form that involves performing simple matrix and
vector operations in terms of idempotent algebra and provides a basis for the
development of efficient computational algorithms and their software
implementation.Comment: Proceedings of the 6th WSEAS European Computing Conference (ECC '12),
Prague, Czech Republic, September 24-26, 201
Almost Block Diagonal Linear Systems: Sequential and Parallel Solution Techniques, and Applications
Almost block diagonal (ABD) linear systems arise in a variety of contexts, specifically in numerical methods for two-point boundary value problems for ordinary differential equations and in related partial differential equation problems. The stable, efficient sequential solution of ABDs has received much attention over the last fifteen years and the parallel solution more recently. We survey the fields of application with emphasis on how ABDs and bordered ABDs (BABDs) arise. We outline most known direct solution techniques, both sequential and parallel, and discuss the comparative efficiency of the parallel methods. Finally, we examine parallel iterative methods for solving BABD systems. Copyright (C) 2000 John Wiley & Sons, Ltd
Graph theory, irreducibility, and structural analysis of differential-algebraic equation systems
The -method for structural analysis of a differential-algebraic
equation (DAE) system produces offset vectors from which the sparsity pattern
of a system Jacobian is derived. This pattern implies a block-triangular form
(BTF) of the DAE that can be exploited to speed up numerical solution.
The paper compares this fine BTF with the usually coarser BTF derived from
the sparsity pattern of the \sigmx. It defines a Fine-Block Graph with weighted
edges, which gives insight into the relation between coarse and fine blocks,
and the permitted ordering of blocks to achieve BTF. It also illuminates the
structure of the set of normalised offset vectors of the DAE, e.g.\ this set is
finite if and only if there is just one coarse block
Canonical forms of multidimensional steady inviscid flows
Canonical forms and canonical variables for inviscid flow problems are derived. In these forms the components of the system governed by different types of operators (elliptic and hyperbolic) are separated. Both the incompressible and compressible cases are analyzed, and their similarities and differences are discussed. The canonical forms obtained are block upper triangular operator form in which the elliptic and non-elliptic parts reside in different blocks. The full nonlinear equations are treated without using any linearization process. This form enables a better analysis of the equations as well as better numerical treatment. These forms are the analog of the decomposition of the one dimensional Euler equations into characteristic directions and Riemann invariants
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