Search results for "MathematicsofComputing_NUMERICALANALYSIS"
showing 10 items of 149 documents
A grid ant colony algorithm for the orienteering problem
2005
In this paper we propose a distributed ant colony algorithm to solve large scale orienteering problem instances. Our approach is based on a multi-colony strategy where each colony works in an independent portion (cluster) in the original graph. This results in no need for communicating pheromones information among colonies and in increasing speedup. We have implemented our algorithm as a .NET Web services infrastructure following a grid computing philosophy and we provide some promising experimental results to show the feasibility and effectiveness of our approach
Stiffness-Adaptive Taylor method for the integration of non-stiff and stiff kinetic models
1992
A systematic derivation procedure that greatly facilitates the application of the Taylor method to the integration of kinetic models is developed. In addition, an algorithm that gives the integration step as a function of the required level of accuracy is proposed. Using the Taylor method, application of this algorithm is immediate and largely reduces the integration time. In addition, a new method of integration of kinetic models, whose most important feature is the self-adaptability to the stiffness of the system along the integration process, is developed. This “stiffness-adaptive” Taylor method (SAT method) makes use of several algorithms, combining them to meet the particular requireme…
Multilayer neural networks: an experimental evaluation of on-line training methods
2004
Artificial neural networks (ANN) are inspired by the structure of biological neural networks and their ability to integrate knowledge and learning. In ANN training, the objective is to minimize the error over the training set. The most popular method for training these networks is back propagation, a gradient descent technique. Other non-linear optimization methods such as conjugate directions set or conjugate gradient have also been used for this purpose. Recently, metaheuristics such as simulated annealing, genetic algorithms or tabu search have been also adapted to this context.There are situations in which the necessary training data are being generated in real time and, an extensive tr…
Non-periodic Discrete-Spline Wavelets
2015
This chapter describes wavelet analysis in the spaces of discrete splines whose spans are powers of 2. This wavelet analysis is similar to wavelet analysis in the polynomial-spline spaces. The transforms are based on relations between exponential discrete splines from different resolution scales. Generators of discrete-spline wavelet spaces are described. The discrete-spline wavelet transforms generate wavelet transforms in signal space. Practically, wavelet transforms of signals are implemented by multirate filtering of signals by two-channel filter banks with the downsampling factor 2 (critically sampled filter banks). The filtering implementation is accelerated by switching to the polyph…
An adaptive method for Volterra–Fredholm integral equations on the half line
2009
AbstractIn this paper we develop a direct quadrature method for solving Volterra–Fredholm integral equations on an unbounded spatial domain. These problems, when related to some important physical and biological phenomena, are characterized by kernels that present variable peaks along space. The method we propose is adaptive in the sense that the number of spatial nodes of the quadrature formula varies with the position of the peaks. The convergence of the method is studied and its performances are illustrated by means of a few significative examples. The parallel algorithm which implements the method and its performances are described.
Gaussian quadrature rule for arbitrary weight function and interval
2005
Abstract A program for calculating abscissas and weights of Gaussian quadrature rules for arbitrary weight functions and intervals is reported. The program is written in Mathematica. The only requirement is that the moments of the weight function can be evaluated analytically in Mathematica. The result is a FORTRAN subroutine ready to be utilized for quadrature. Program summary Title of program: AWGQ Catalogue identifier:ADVB Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVB Program obtained from: CPC Program Library, Queens University, Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Pentium IV 1.7 GHz processor Ins…
Polynomial Spline-Wavelets
2015
This chapter presents wavelets in the spaces of polynomial splines. The wavelets’ design is based on the Zak transform, which provides an integral representation of spline-wavelets. The exponential wavelets which participate in the integral representation are counterparts of the exponential splines that were introduced in Chap. 4. Fast algorithms for the wavelet transforms of splines are presented. Generators of spline-wavelet spaces are described, such as the B-wavelets and their duals and the Battle-Lemarie wavelets whose shifts form orthonormal bases of the spline-wavelet spaces.
An interactive surrogate-based method for computationally expensive multiobjective optimisation
2019
Many disciplines involve computationally expensive multiobjective optimisation problems. Surrogate-based methods are commonly used in the literature to alleviate the computational cost. In this paper, we develop an interactive surrogate-based method called SURROGATE-ASF to solve computationally expensive multiobjective optimisation problems. This method employs preference information of a decision-maker. Numerical results demonstrate that SURROGATE-ASF efficiently provides preferred solutions for a decision-maker. It can handle different types of problems involving for example multimodal objective functions and nonconvex and/or disconnected Pareto frontiers. peerReviewed
Attractor as a convex combination of a set of attractors
2021
This paper presents an effective approach to constructing numerical attractors of a general class of continuous homogenous dynamical systems: decomposing an attractor as a convex combination of a set of other existing attractors. For this purpose, the convergent Parameter Switching (PS) numerical method is used to integrate the underlying dynamical system. The method is built on a convergent fixed step-size numerical method for ODEs. The paper shows that the PS algorithm, incorporating two binary operations, can be used to approximate any numerical attractor via a convex combination of some existing attractors. Several examples are presented to show the effectiveness of the proposed method.…
Predictive control of convex polyhedron LPV systems with Markov jumping parameters
2012
The problem of receding horizon predictive control of stochastic linear parameter varying systems is discussed. First, constant coefficient matrices are obtained at each vertex in the interior of linear parameter varying system, and then, by considering semi-definite programming constraints, weight coefficients between each vertex are calculated, and the equal coefficients matrices for the time variable system are obtained. Second, in the given receding horizon, for each mode sequence of the stochastic convex polyhedron linear parameter varying systems, the optimal control input sequences are designed in order to make the states into a terminal invariant set. Outside of the receding horizon…