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At least 73 records · Page 4Linked to original sources
arXiv2009

Global communications in multiprocessor simulations of flames

In this paper we investigate performance of global communications in a particular parallel code. The code simulates dynamics of expansion of premixed spherical flames using an asymptotic model of Sivashinsky type and a spectral numerical algorithm. As a result, the code heavily relies on global all-to-all interprocessor communications implementing transposition of the distributed data array in which numerical solution to the problem is stored. This global data interdependence makes interprocessor connectivity of the HPC system as important as the floating-point power of the processors of which the system is built. Our experiments show that efficient numerical simulation of this particular model, with global data interdependence, on modern HPC systems is possible. Prospects of performance of more sophisticated models of flame dynamics are analysed as well.

cs.DC↗
arXiv2009

NetEvo: A computational framework for the evolution of dynamical complex networks

NetEvo is a computational framework designed to help understand the evolution of dynamical complex networks. It provides flexible tools for the simulation of dynamical processes on networks and methods for the evolution of underlying topological structures. The concept of a supervisor is used to bring together both these aspects in a coherent way. It is the job of the supervisor to rewire the network topology and alter model parameters such that a user specified performance measure is minimised. This performance measure can make use of current topological information and simulated dynamical output from the system. Such an abstraction provides a suitable basis in which to study many outstanding questions related to complex system design and evolution.

cs.MS↗
arXiv2019

JBotSim, a Tool for Fast Prototyping of Distributed Algorithms in Dynamic Networks

JBotSim is a java library that offers basic primitives for prototyping, running, and visualizing distributed algorithms in dynamic networks. With JBotSim, one can implement an idea in minutes and interact with it ({\it e.g. }, add, move, or delete nodes) while it is running. JBotSim is well suited to prepare live demonstrations of your algorithms to colleagues or students; it can also be used to evaluate performance at the algorithmic level (number of messages, number of rounds, etc.). Unlike most tools, JBotSim is not an integrated environment. It is a lightweight library to be used in your program. In this paper, we present an overview of its distinctive features and architecture.

cs.MS↗
arXiv2010

Algorithmic Differentiation of Linear Algebra Functions with Application in Optimum Experimental Design (Extended Version)

We derive algorithms for higher order derivative computation of the rectangular $QR$ and eigenvalue decomposition of symmetric matrices with distinct eigenvalues in the forward and reverse mode of algorithmic differentiation (AD) using univariate Taylor propagation of matrices (UTPM). Linear algebra functions are regarded as elementary functions and not as algorithms. The presented algorithms are implemented in the BSD licensed AD tool \texttt{ALGOPY}. Numerical tests show that the UTPM algorithms derived in this paper produce results close to machine precision accuracy. The theory developed in this paper is applied to compute the gradient of an objective function motivated from optimum experimental design: $\nabla_x Φ(C(J(F(x,y))))$, where $Φ= \{λ_1 : λ_1 C\}$, $C = (J^T J)^{-1}$, $J = \frac{\dd F}{\dd y}$ and $F = F(x,y)$.

cs.DS↗
arXiv2012

Using Premia and Nsp for Constructing a Risk Management Benchmark for Testing Parallel Architecture

Financial institutions have massive computations to carry out overnight which are very demanding in terms of the consumed CPU. The challenge is to price many different products on a cluster-like architecture. We have used the Premia software to valuate the financial derivatives. In this work, we explain how Premia can be embedded into Nsp, a scientific software like Matlab, to provide a powerful tool to valuate a whole portfolio. Finally, we have integrated an MPI toolbox into Nsp to enable to use Premia to solve a bunch of pricing problems on a cluster. This unified framework can then be used to test different parallel architectures.

cs.CE↗
arXiv2010

An in-place truncated Fourier transform and applications to polynomial multiplication

The truncated Fourier transform (TFT) was introduced by van der Hoeven in 2004 as a means of smoothing the "jumps" in running time of the ordinary FFT algorithm that occur at power-of-two input sizes. However, the TFT still introduces these jumps in memory usage. We describe in-place variants of the forward and inverse TFT algorithms, achieving time complexity O(n log n) with only O(1) auxiliary space. As an application, we extend the second author's results on space-restricted FFT-based polynomial multiplication to polynomials of arbitrary degree.

cs.DS↗
arXiv2010

The Power of Vocabulary: The Case of Cyclotomic Polynomials

We observe that the vocabulary used to construct the "answer" to problems in computer algebra can have a dramatic effect on the computational complexity of solving that problem. We recall a formalization of this observation and explain the classic example of sparse polynomial arithmetic. For this case, we show that it is possible to extend the vocabulary so as reap the benefits of conciseness whilst avoiding the obvious pitfall of repeating the problem statement as the "solution". It is possible to extend the vocabulary either by irreducible cyclotomics or by $x^n-1$: we look at the options and suggest that the pragmatist might opt for both.

cs.SC↗
arXiv2010

Assessment Of The Wind Farm Impact On The Radar

This study shows the means to evaluate the wind farm impact on the radar. It proposes the set of tools, which can be used to realise this objective. The big part of report covers the study of complex pattern propagation factor as the critical issue of the Advanced Propagation Model (APM). Finally, the reader can find here the implementation of this algorithm - the real scenario in Inverness airport (the United Kingdom), where the ATC radar STAR 2000, developed by Thales Air Systems, operates in the presence of several wind farms. Basically, the project is based on terms of the department "Strategy Technology & Innovation", where it has been done. Also you can find here how the radar industry can act with the problem engendered by wind farms. The current strategies in this area are presented, such as a wind turbine production, improvements of air traffic handling procedures and the collaboration between developers of radars and wind turbines. The possible strategy for Thales as a main pioneer was given as well.

cs.CV↗
arXiv2010

Factorization of Non-Commutative Polynomials

We describe an algorithm for the factorization of non-commutative polynomials over a field. The first sketch of this algorithm appeared in an unpublished manuscript (literally hand written notes) by James H. Davenport more than 20 years ago. This version of the algorithm contains some improvements with respect to the original sketch. An improved version of the algorithm has been fully implemented in the Axiom computer algebra system.

cs.MS↗
arXiv2010

Towards an Efficient Tile Matrix Inversion of Symmetric Positive Definite Matrices on Multicore Architectures

The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research has shown that it is possible to write efficient and scalable tile algorithms for performing a Cholesky factorization, a (pseudo) LU factorization, and a QR factorization. In this extended abstract, we attack the problem of the computation of the inverse of a symmetric positive definite matrix. We observe that, using a dynamic task scheduler, it is relatively painless to translate existing LAPACK code to obtain a ready-to-be-executed tile algorithm. However we demonstrate that non trivial compiler techniques (array renaming, loop reversal and pipelining) need then to be applied to further increase the parallelism of our application. We present preliminary experimental results.

cs.MS↗
arXiv2010

Triangular Decomposition of Semi-algebraic Systems

Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue: semi-algebraic systems. We show that any such system can be decomposed into finitely many {\em regular semi-algebraic systems}. We propose two specifications of such a decomposition and present corresponding algorithms. Under some assumptions, one type of decomposition can be computed in singly exponential time w.r.t.\ the number of variables. We implement our algorithms and the experimental results illustrate their effectiveness.

cs.SC↗
arXiv2018

Having Fun with Lambert W(x) Function

This short note presents the Lambert W(x) function and its possible application in the framework of physics related to the Pierre Auger Observatory. The actual numerical implementation in C++ consists of Halley's and Fritsch's iteration with branch-point expansion, asymptotic series and rational fits as initial approximations.

cs.MS↗
arXiv2010

Efficient Construction, Update and Downdate Of The Coefficients Of Interpolants Based On Polynomials Satisfying A Three-Term Recurrence Relation

In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the interpolation incrementally and can be used to update the coefficients whenever a nodes is added to or removed from the interpolation. The second algorithm, which constructs the interpolation coefficients by decomposing the Vandermonde-like matrix iteratively, can not be used to update or downdate an interpolation, yet is more numerically stable than the first algorithm and is more efficient when the coefficients of multiple interpolations are to be computed over the same set of nodes.

math.NA↗
arXiv2010

A Review of Error Estimation in Adaptive Quadrature

The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated and discussed. This paper presents a review of existing error estimation techniques and discusses their differences and their common features. Some common shortcomings of these algorithms are discussed and a new general error estimation technique is presented.

math.NA↗
arXiv2010

wiki.openmath.org - how it works, how you can participate

At http://wiki.openmath.org, the OpenMath 2 and 3 Content Dictionaries are accessible via a semantic wiki interface, powered by the SWiM system. We shortly introduce the inner workings of the system, then describe how to use it, and conclude with first experiences gained from OpenMath society members working with the system and an outlook to further development plans.

cs.DL↗
arXiv2011

Computational Complexity of Iterated Maps on the Interval

The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. There are two main results. First, the computational complexity measure considered here is related to the Lyapunov exponent of the dynamical system under consideration. Second, the presented algorithm is optimal with regard to that complexity measure.

math.NA↗